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    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingAbstract"/>
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    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
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    <link:label id="lab_srt_MaximumMember_019eb2fa-0349-76f4-b842-b7e29e5f904b_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MaximumMember"/>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member_019eb2fa-026d-7328-b0ff-dde307563e19_terseLabel_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing September 15, 2025 to December 31, 2026</link:label>
    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member_label_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing September 15, 2025 to December 31, 2026 [Member]</link:label>
    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member_documentation_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingSeptember152025ToDecember312026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing September 15, 2025 to December 31, 2026</link:label>
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    <link:label id="lab_srt_RangeMember_019eb2fa-026d-7a59-871b-bdf096e606b0_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_019eb2fa-0349-7349-88ad-1896ff21371e_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_019eb2fa-0349-7ae6-9a50-cc01e2e4b843_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to Class A Common Stockholders&#8212;diluted</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019eb2fa-03d6-744f-8f03-ab292ba006a2_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019eb2fa-026d-7920-854c-06934a902adc_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_019eb2fa-0349-7b5e-99d0-27cd21916b0a_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, performance obligation expected timing of satisfaction period</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_019eb2fa-03d6-789e-b645-db428694cf1e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition-related costs</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition-Related Cost, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAcquisitionRelatedCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:to="lab_us-gaap_BusinessCombinationAcquisitionRelatedCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_019eb2fa-0349-77d2-948e-0a4e1511d92c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average interest rate</link:label>
    <link:label id="lab_us-gaap_DebtWeightedAverageInterestRate_label_en-US" xlink:label="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt, Weighted Average Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtWeightedAverageInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtWeightedAverageInterestRate" xlink:to="lab_us-gaap_DebtWeightedAverageInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MajorCustomersAxis_019eb2fa-0349-7e6e-8dce-ae4380b1547f_terseLabel_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:label id="lab_srt_MajorCustomersAxis_label_en-US" xlink:label="lab_srt_MajorCustomersAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MajorCustomersAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MajorCustomersAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MajorCustomersAxis" xlink:to="lab_srt_MajorCustomersAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019eb2fa-0349-745f-9ae2-c581e525d656_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Future Amortization of Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, and Capitalized Cost, Software to be Sold, Leased, or Marketed, Estimated Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ReceivablesLongTermContractsOrPrograms_label_en-US" xlink:label="lab_us-gaap_ReceivablesLongTermContractsOrPrograms" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables, Long-Term Contracts or Programs</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
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    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_019eb2fa-03d6-7727-ae5e-b95d9e7e385e_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and benefits</link:label>
    <link:label id="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee-related Liabilities, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:to="lab_us-gaap_EmployeeRelatedLiabilitiesCurrent" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationExpectedTimingOfSatisfactionStartDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]</link:label>
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    <link:label id="lab_us-gaap_LineOfCreditMember_019eb2fa-03d6-7b3c-a1f4-a5f10fcedf6c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of Credit</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditMember" xlink:to="lab_us-gaap_LineOfCreditMember" xlink:type="arc" order="1"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_019eb2fa-0349-7d39-9b49-5f0cb540fe84_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
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    <link:label id="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_019eb2fa-0349-7a41-b779-40db03fb639b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effective Income Tax Rate Reconciliation</link:label>
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    <link:label id="lab_us-gaap_GoodwillLineItems_019eb2fa-0349-7777-ba9d-1550cdaa81bd_verboseLabel_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
    <link:label id="lab_us-gaap_GoodwillLineItems_label_en-US" xlink:label="lab_us-gaap_GoodwillLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Line Items]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019eb2fa-0349-7f44-b10e-3d978ea638f2_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_019eb2fa-026d-75c0-8f68-797b1db70273_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Finance lease payments</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member_019eb2fa-0349-7310-ba0c-e1f0a9213475_terseLabel_en-US" xlink:label="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3.4396% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:label id="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member_label_en-US" xlink:label="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.4396% Interest Rate Swap, Maturing at December 2026 [Member]</link:label>
    <link:label id="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member_documentation_en-US" xlink:label="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.4396% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:href="lgn-20260630.xsd#lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:to="lab_lgn_A3.4396InterestRateSwapMaturingAtDecember2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum_019eb2fa-03d6-7a1f-be6c-2cbcea5321e9_terseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, covenant, minimum availability milestone of facility size (as percent)</link:label>
    <link:label id="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum_label_en-US" xlink:label="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Threshold To Test Net Leverage Ratio, Outstanding Borrowings Compared To Facility Size, Percent, Minimum</link:label>
    <link:label id="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Threshold To Test Net Leverage Ratio, Outstanding Borrowings Compared To Facility Size, Percent, Minimum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:to="lab_lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_019eb2fa-0349-79ee-8ed8-06ead1e4d557_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesTable_019eb2fa-026d-7a92-ad76-74f3d97dd451_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesTable" xlink:to="lab_us-gaap_LossContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementNetLiability_019eb2fa-0349-75a6-9d90-ac754a1f98b2_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementNetLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax receivable agreement liability and deferred taxes arising from exchanges of Class B Common Stock</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementNetLiability_019eb2fa-0349-74d6-b87f-4d0b94658c03_negatedTerseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementNetLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Tax receivable agreement liability and deferred taxes arising from exchanges of Class B Common Stock</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementNetLiability_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementNetLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Net Liability</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementNetLiability_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementNetLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Net Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementNetLiability" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementNetLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementNetLiability" xlink:to="lab_lgn_TaxReceivableAgreementNetLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_019eb2fa-03d6-7eac-9723-29f036e8ed32_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss), net:</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum_019eb2fa-0349-7ba7-be98-7c0ee390dac4_terseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, covenant, ratio of consolidated first lien net leverage ratio</link:label>
    <link:label id="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum_label_en-US" xlink:label="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Consolidated First Lien Net Leverage Ratio, Maximum</link:label>
    <link:label id="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Covenant, Consolidated First Lien Net Leverage Ratio, Maximum</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:to="lab_lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment_019f87e5-5064-7986-baea-2b81f371e345_terseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable rate (as percent)</link:label>
    <link:label id="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment_label_en-US" xlink:label="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate, Adjustment</link:label>
    <link:label id="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:to="lab_lgn_DebtInstrumentBasisSpreadOnVariableRateAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_019eb2fa-026d-74fa-9d34-2e4f820fced4_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A Common Stock for acquisitions</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019eb2fa-026d-7a9e-9488-96e7e48cb2ad_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019eb2fa-0349-7f39-a070-4eeaa139e307_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrecurringAdjustmentAxis_019eb2fa-03d6-7f33-806d-ff7298b992f1_terseLabel_en-US" xlink:label="lab_us-gaap_NonrecurringAdjustmentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment [Axis]</link:label>
    <link:label id="lab_us-gaap_NonrecurringAdjustmentAxis_label_en-US" xlink:label="lab_us-gaap_NonrecurringAdjustmentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrecurringAdjustmentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrecurringAdjustmentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrecurringAdjustmentAxis" xlink:to="lab_us-gaap_NonrecurringAdjustmentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination_019eb2fa-0349-7b7c-9fd5-546d2ea170b3_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Increase (Decrease) for Contract Acquired in Business Combination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_019eb2fa-026d-7f80-8422-d1d03b6c395a_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019eb2fa-0349-7718-8639-e23f3f77c339_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019eb2fa-0349-7207-9518-032645d004de_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued and other current liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_019eb2fa-0349-7a61-953e-c1a60543e1cb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxContingencyLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxContingencyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxContingencyLineItems" xlink:to="lab_us-gaap_IncomeTaxContingencyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_019eb2fa-0349-7445-832d-49398d155212_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notional amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_019eb2fa-0349-7e0a-89f6-12e15c1e2df8_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Notional Amount</link:label>
    <link:label id="lab_us-gaap_DerivativeNotionalAmount_label_en-US" xlink:label="lab_us-gaap_DerivativeNotionalAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Notional Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeNotionalAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeNotionalAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeNotionalAmount" xlink:to="lab_us-gaap_DerivativeNotionalAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019eb2fa-0349-7779-b51c-2ccc753201cc_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019eb2fa-0349-7c5e-bd2f-88850c85f0df_verboseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average Class A Common Stock outstanding&#8212;basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_019eb2fa-0349-7df6-854e-832b282a9fa8_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets, net</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetNetCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:to="lab_us-gaap_ContractWithCustomerAssetNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_019eb2fa-026d-70fb-919c-3defe0520b4a_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated goodwill impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impaired, Accumulated Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillImpairedAccumulatedImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairedAccumulatedImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_019eb2fa-026d-72c5-90f9-92fad8eee1de_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember_019eb2fa-026d-76c1-81e7-e754ea12079d_terseLabel_en-US" xlink:label="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Jefferies Finance LLC Revolving Line Of Credit</link:label>
    <link:label id="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember_label_en-US" xlink:label="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Jefferies Finance LLC Revolving Line Of Credit [Member]</link:label>
    <link:label id="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember_documentation_en-US" xlink:label="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Jefferies Finance LLC Revolving Line Of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:href="lgn-20260630.xsd#lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:to="lab_lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_019eb2fa-03d6-75d7-adea-8e49b9f81521_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reportable segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_019eb2fa-0349-7d46-9b7f-8c166e5000b0_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member_019eb2fa-026d-7ceb-9d2b-c801af31a376_terseLabel_en-US" xlink:label="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3.2480% Interest Rate Swap, Maturing at December 2027</link:label>
    <link:label id="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member_label_en-US" xlink:label="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.2480% Interest Rate Swap, Maturing at December 2027 [Member]</link:label>
    <link:label id="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member_documentation_en-US" xlink:label="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.2480% Interest Rate Swap, Maturing at December 2027</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:href="lgn-20260630.xsd#lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:to="lab_lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_019eb2fa-026d-7409-8081-93efc8f8c471_periodStartLabel_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_019eb2fa-026d-71f9-897c-90e1b41a6a30_periodEndLabel_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Limited Liability Company (LLC) Members' Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_LimitedLiabilityCompanyLlcMembersEquityIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_019eb2fa-026d-7249-a5f8-a5c2c79e62f7_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelationshipsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelationshipsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Relationships [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerRelationshipsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerRelationshipsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelationshipsMember" xlink:to="lab_us-gaap_CustomerRelationshipsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_SaleOfStockOptionPeriod_019eb2fa-0349-7811-967a-96904bcc2e7a_terseLabel_en-US" xlink:label="lab_lgn_SaleOfStockOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock option period</link:label>
    <link:label id="lab_lgn_SaleOfStockOptionPeriod_label_en-US" xlink:label="lab_lgn_SaleOfStockOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock Option Period</link:label>
    <link:label id="lab_lgn_SaleOfStockOptionPeriod_documentation_en-US" xlink:label="lab_lgn_SaleOfStockOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock Option Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_SaleOfStockOptionPeriod" xlink:href="lgn-20260630.xsd#lgn_SaleOfStockOptionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_SaleOfStockOptionPeriod" xlink:to="lab_lgn_SaleOfStockOptionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019eb2fa-0349-7490-a688-cc3f6b09909f_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019eb2fa-0349-7a0a-9151-ecc230858f77_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Additional Cash Flow Information</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow, Supplemental Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained_019eb2fa-026d-7eac-97b6-a436e81f59e8_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash tax savings retained (as a percent)</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Cash Tax Savings Retained</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Cash Tax Savings Retained</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementCashTaxSavingsRetained"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:to="lab_lgn_TaxReceivableAgreementCashTaxSavingsRetained" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_019eb2fa-03d6-79e6-96cb-1f7dc33fd1f6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationLineItems_019eb2fa-03d6-7421-960a-e6ee69e8d773_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:label id="lab_dei_DocumentInformationLineItems_label_en-US" xlink:label="lab_dei_DocumentInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationLineItems" xlink:to="lab_dei_DocumentInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiDiscTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiDiscTextBlock" xlink:to="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_019eb2fa-0349-79ff-a4ff-fda79bd0858d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementClassOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementClassOfStockAxis" xlink:to="lab_us-gaap_StatementClassOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019eb2fa-0349-74f1-8226-567cccff2c12_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_019eb2fa-0349-76a4-934a-326b5d922d31_totalLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNet_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, after Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_019eb2fa-0349-7429-90bf-86cd794831f6_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate (as percent)</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Interest Rate at Period End</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:to="lab_us-gaap_LineOfCreditFacilityInterestRateAtPeriodEnd" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019eb2fa-0349-7f52-b55c-9d7950555fab_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to Legence&#8212;basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019eb2fa-0349-7560-bc4c-7be008978aa2_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to Class A Common Stockholders&#8212;basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerMember_019eb2fa-03d6-7a98-a895-e5875f4c3a1a_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer Benchmark</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerMember_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer Benchmark [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerMember" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares_019eb2fa-0349-726d-84b5-b0976bf6e030_terseLabel_en-US" xlink:label="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchanged shares (in shares)</link:label>
    <link:label id="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares_label_en-US" xlink:label="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Number Of Shares Issued In Transaction, Exchanged Shares</link:label>
    <link:label id="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares_documentation_en-US" xlink:label="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Sale Of Stock, Number Of Shares Issued In Transaction, Exchanged Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:href="lgn-20260630.xsd#lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:to="lab_lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019eb2fa-026d-7c3d-872b-33ded43d460e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_019eb2fa-0349-7840-90f6-20d51c949998_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_019eb2fa-0349-7f98-af8c-c84862babeeb_terseLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other expense (income):</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_NonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_019eb2fa-026d-7146-a830-494859f2058c_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, maximum borrowing capacity</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementTextBlock_019eb2fa-0349-7099-86f1-bd1d9a5f2492_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementTextBlock_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement [Text Block]</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementTextBlock_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementTextBlock" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementTextBlock" xlink:to="lab_lgn_TaxReceivableAgreementTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019eb2fa-026d-7547-b0c7-6aa946375680_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_019eb2fa-026d-779b-965a-17b0cff3ac7b_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019eb2fa-0349-71b2-86e1-086673763807_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_019eb2fa-0349-7244-a95b-2bfea3921ce5_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (loss) related to interest rate swaps, net of tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Cash Flow Hedge, Gain (Loss), after Reclassification and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossCashFlowHedgeGainLossAfterReclassificationAndTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019eb2fa-03d6-7e92-ae3f-cb682fdc538b_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019eb2fa-03d6-71b7-808f-5a183b98b2e6_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_019eb2fa-0349-7e52-87ea-857e0c09a699_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019eb2fa-0349-70b6-aedd-46a4d703a7f7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_019eb2fa-03d6-78cf-aea6-fd232c4e15c4_terseLabel_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non- controlling Interests</link:label>
    <link:label id="lab_us-gaap_NoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestMember" xlink:to="lab_us-gaap_NoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_019eb2fa-03d6-7666-9759-c6d33d46d82f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Gain on sale of property and equipment</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019eb2fa-0349-71bd-a8c6-ff0479f8236c_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback_019eb2fa-0349-7018-84e9-d9676dd1f881_terseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Holdback</link:label>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback_label_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Incurred, Holdback</link:label>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Liabilities Incurred, Holdback</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:to="lab_lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_019eb2fa-0349-730f-b338-0b71054e3b49_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterestDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestDisclosureTextBlock" xlink:to="lab_us-gaap_MinorityInterestDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_019eb2fa-0349-7497-b50a-9e16a841d561_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Revolver payments</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_019eb2fa-0349-78ae-8f4a-4beef28b04c5_terseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolver payments</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfLinesOfCredit" xlink:to="lab_us-gaap_RepaymentsOfLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember_019eb2fa-0349-788d-94a4-61f665c51808_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Cash Flow Hedge, Including Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Cash Flow Hedge, Including Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:to="lab_us-gaap_AccumulatedGainLossCashFlowHedgeIncludingNoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MemberUnitsMember_019eb2fa-03d6-7ec8-bcc4-898bbbb98a10_terseLabel_en-US" xlink:label="lab_us-gaap_MemberUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Member's Equity</link:label>
    <link:label id="lab_us-gaap_MemberUnitsMember_label_en-US" xlink:label="lab_us-gaap_MemberUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Member Units [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MemberUnitsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MemberUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MemberUnitsMember" xlink:to="lab_us-gaap_MemberUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TimeInterestsMember_019eb2fa-0349-7b8b-8471-2cdd53a6a876_terseLabel_en-US" xlink:label="lab_lgn_TimeInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Time Interests</link:label>
    <link:label id="lab_lgn_TimeInterestsMember_label_en-US" xlink:label="lab_lgn_TimeInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Time Interests [Member]</link:label>
    <link:label id="lab_lgn_TimeInterestsMember_documentation_en-US" xlink:label="lab_lgn_TimeInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Time Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TimeInterestsMember" xlink:href="lgn-20260630.xsd#lgn_TimeInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TimeInterestsMember" xlink:to="lab_lgn_TimeInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerRelatedIntangibleAssetsMember_019eb2fa-0349-711e-b6a0-8273d46e3a72_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerRelatedIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer relationships</link:label>
    <link:label id="lab_us-gaap_CustomerRelatedIntangibleAssetsMember_label_en-US" xlink:label="lab_us-gaap_CustomerRelatedIntangibleAssetsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer-Related Intangible Assets [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerRelatedIntangibleAssetsMember" xlink:to="lab_us-gaap_CustomerRelatedIntangibleAssetsMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_019eb2fa-026d-7968-b07c-a44ffefe9ef5_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019eb2fa-0349-7906-8745-af257025b703_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash used in investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
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    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member_019eb2fa-0349-781a-b715-c934bcbf8492_terseLabel_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member_label_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing at December 2026 [Member]</link:label>
    <link:label id="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member_documentation_en-US" xlink:label="lab_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">4.0433% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member" xlink:href="lgn-20260630.xsd#lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_019eb2fa-0349-726f-a282-13abf850863e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019eb2fa-026d-75f3-af40-dd842f61f53f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_019eb2fa-026d-73c3-a714-bff4595095a5_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Contract with Customer, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInContractWithCustomerAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:to="lab_us-gaap_IncreaseDecreaseInContractWithCustomerAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_019eb2fa-026d-7eb8-bc1f-2994e2571753_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019eb2fa-0349-7984-a52d-772d0f2485fb_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_019eb2fa-026d-7fc0-9ee7-a70734296bef_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, term (in years)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTerm_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTerm" xlink:to="lab_us-gaap_DebtInstrumentTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_019eb2fa-0349-728e-bba9-6fbeaf887ece_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net of current portion</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Long-Term Debt, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNoncurrentLiabilitiesLongTermDebt"/>
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    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_019eb2fa-03d6-761b-b2c6-9d642f20670c_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation allowance, deferred tax asset, increase (decrease), amount</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_019eb2fa-0349-76f7-85e7-59bab57fdc8b_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income (loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_dei_EntityShellCompany_019eb2fa-03d6-7ab0-8dd8-fbe2ba03a061_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityShellCompany"/>
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    <link:label id="lab_us-gaap_CommonClassBMember_019eb2fa-03d6-785f-b634-e3ec13d72adc_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class B</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_019eb2fa-03d6-7e09-b167-08d2ee02dbc3_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Class B Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonClassBMember_label_en-US" xlink:label="lab_us-gaap_CommonClassBMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class B [Member]</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_019eb2fa-0349-722a-be74-f7f04795aae7_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of operating lease liabilities (including $3,889 and $3,920 as of June&#160;30, 2026 and December&#160;31, 2025, respectively, from related parties)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityCurrent"/>
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    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
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    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019eb2fa-03d6-744b-b8f7-62398804e040_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSoldAbstract_019eb2fa-026d-77bd-80be-d2057fccd999_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSoldAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue:</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSoldAbstract_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSoldAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Product and Service Sold [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSoldAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfGoodsAndServicesSoldAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSoldAbstract" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSoldAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_019eb2fa-0349-7c38-87ca-1711a7e94588_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss per share:</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019eb2fa-0349-77b5-ba30-ecf45cd08449_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityCurrent_019eb2fa-03d6-7eb0-807c-7d56dcab1ac5_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current portion of tax receivable agreement liability - related party</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityCurrent_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Current</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityCurrent_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:to="lab_lgn_TaxReceivableAgreementLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill_019eb2fa-0349-73bd-a78e-c224a57c17cd_totalLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Asset</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets Acquired Including Goodwill</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Identifiable Assets Acquired and Liabilities Assumed, Assets Acquired Including Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:to="lab_lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019eb2fa-03d6-7943-ba1c-9905a7266cc5_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_019eb2fa-03d6-7533-82eb-398e2b388160_terseLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019eb2fa-0349-7272-b9a8-4ccf3ff237b6_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_CompensationExpensePerformanceInterests_019eb2fa-0349-714d-a130-54a9881c7582_terseLabel_en-US" xlink:label="lab_lgn_CompensationExpensePerformanceInterests" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation expense - Performance Interests</link:label>
    <link:label id="lab_lgn_CompensationExpensePerformanceInterests_label_en-US" xlink:label="lab_lgn_CompensationExpensePerformanceInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Expense, Performance Interests</link:label>
    <link:label id="lab_lgn_CompensationExpensePerformanceInterests_documentation_en-US" xlink:label="lab_lgn_CompensationExpensePerformanceInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Compensation Expense, Performance Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_CompensationExpensePerformanceInterests" xlink:href="lgn-20260630.xsd#lgn_CompensationExpensePerformanceInterests"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_CompensationExpensePerformanceInterests" xlink:to="lab_lgn_CompensationExpensePerformanceInterests" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_019eb2fa-03d6-71c6-ace3-a1422a1be56b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_019eb2fa-026d-7e0f-9af1-4da62d2266fc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Swap Agreements</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Interest Rate Derivatives [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfInterestRateDerivativesTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_019eb2fa-026d-74e6-942d-630afe39d00a_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator&#8212;basic:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_019eb2fa-0349-7427-bc12-cfa91cbfd653_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Asset and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureName_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureName_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureName" xlink:to="lab_ecd_CoSelectedMeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_019eb2fa-0349-769c-9cd9-fe59d83ad5fa_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_Total2025AcquisitionsMember_019eb2fa-0349-737f-85fb-b2608827da42_terseLabel_en-US" xlink:label="lab_lgn_Total2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total 2025 Acquisitions</link:label>
    <link:label id="lab_lgn_Total2025AcquisitionsMember_label_en-US" xlink:label="lab_lgn_Total2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total 2025 Acquisitions [Member]</link:label>
    <link:label id="lab_lgn_Total2025AcquisitionsMember_documentation_en-US" xlink:label="lab_lgn_Total2025AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total 2025 Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_Total2025AcquisitionsMember" xlink:href="lgn-20260630.xsd#lgn_Total2025AcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_Total2025AcquisitionsMember" xlink:to="lab_lgn_Total2025AcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_019eb2fa-0349-797a-9d9f-adb0830a38cf_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of debt issuance costs and discounts</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs and Discounts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfFinancingCostsAndDiscounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:to="lab_us-gaap_AmortizationOfFinancingCostsAndDiscounts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_019eb2fa-026d-72e7-9fc7-dcc74400885e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed Interest Rate</link:label>
    <link:label id="lab_us-gaap_DerivativeFixedInterestRate_label_en-US" xlink:label="lab_us-gaap_DerivativeFixedInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative, Fixed Interest Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeFixedInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeFixedInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeFixedInterestRate" xlink:to="lab_us-gaap_DerivativeFixedInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease_019ff5ed-ee6d-791f-9b3e-6de77d6a510f_negatedTerseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Additional interest rate (as percent)</link:label>
    <link:label id="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease_label_en-US" xlink:label="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Protentional Additional Increase (Decrease)</link:label>
    <link:label id="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Protentional Additional Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:to="lab_lgn_DebtInstrumentInterestRateProtentionalAdditionalIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_LGNBUnitsMember_019eb2fa-03d6-7383-85e8-d8ad3b0bfadc_terseLabel_en-US" xlink:label="lab_lgn_LGNBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LGN B Units</link:label>
    <link:label id="lab_lgn_LGNBUnitsMember_label_en-US" xlink:label="lab_lgn_LGNBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">LGN B Units [Member]</link:label>
    <link:label id="lab_lgn_LGNBUnitsMember_documentation_en-US" xlink:label="lab_lgn_LGNBUnitsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">LGN B Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_LGNBUnitsMember" xlink:href="lgn-20260630.xsd#lgn_LGNBUnitsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_LGNBUnitsMember" xlink:to="lab_lgn_LGNBUnitsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_019eb2fa-026d-7960-8992-8d965739aa52_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legence's ownership of Legence Holdings Common Units (as percent)</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByParent_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019eb2fa-026d-7694-9df6-08ff00c3d42c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019eb2fa-026d-73a6-ba31-b7d09a785d29_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, gross</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_019eb2fa-0349-743f-b601-86cb815721ab_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasicLineItems_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two Class Method [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasicLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasicLineItems" xlink:to="lab_us-gaap_EarningsPerShareBasicLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_InstallationAndMaintenanceMember_019eb2fa-026d-77b4-a026-ab389de4018a_terseLabel_en-US" xlink:label="lab_lgn_InstallationAndMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Installation &amp; Maintenance</link:label>
    <link:label id="lab_lgn_InstallationAndMaintenanceMember_label_en-US" xlink:label="lab_lgn_InstallationAndMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Installation And Maintenance [Member]</link:label>
    <link:label id="lab_lgn_InstallationAndMaintenanceMember_documentation_en-US" xlink:label="lab_lgn_InstallationAndMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Installation And Maintenance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_InstallationAndMaintenanceMember" xlink:href="lgn-20260630.xsd#lgn_InstallationAndMaintenanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_InstallationAndMaintenanceMember" xlink:to="lab_lgn_InstallationAndMaintenanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityDomain_019eb2fa-0349-7365-967d-23c435055345_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_019eb2fa-026d-7559-922c-4065aad0ddf7_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation and amortization</link:label>
    <link:label id="lab_us-gaap_DepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_DepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Depletion and Amortization, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAndAmortization" xlink:to="lab_us-gaap_DepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019eb2fa-0349-7d9c-b2c6-86b336a21936_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_019eb2fa-0349-78f0-8603-66958e1e62e4_terseLabel_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable&#8212;other</link:label>
    <link:label id="lab_us-gaap_OtherReceivablesNetCurrent_label_en-US" xlink:label="lab_us-gaap_OtherReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Receivables, Net, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherReceivablesNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherReceivablesNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherReceivablesNetCurrent" xlink:to="lab_us-gaap_OtherReceivablesNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019eb2fa-0349-77df-a916-fc10997819ca_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019eb2fa-0349-75d4-83f2-ba1e9fcfd658_totalLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Weighted-average Class A Common Stock outstanding&#8212;diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_019eb2fa-0349-7d18-8fea-efef7ba8027c_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueLineItems_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueLineItems" xlink:to="lab_us-gaap_DisaggregationOfRevenueLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrderOrProductionBacklogMember_019eb2fa-0349-7abc-b085-399a911b82f6_terseLabel_en-US" xlink:label="lab_us-gaap_OrderOrProductionBacklogMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract backlog</link:label>
    <link:label id="lab_us-gaap_OrderOrProductionBacklogMember_label_en-US" xlink:label="lab_us-gaap_OrderOrProductionBacklogMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Order or Production Backlog [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrderOrProductionBacklogMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrderOrProductionBacklogMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrderOrProductionBacklogMember" xlink:to="lab_us-gaap_OrderOrProductionBacklogMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019eb2fa-0349-7fa4-a8b8-324c8fab442d_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_019eb2fa-0349-7a69-8238-4fec5c44c702_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_019eb2fa-0349-76ab-b35f-7889fe51f2a9_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolver borrowings</link:label>
    <link:label id="lab_us-gaap_ProceedsFromLinesOfCredit_label_en-US" xlink:label="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Lines of Credit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromLinesOfCredit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromLinesOfCredit" xlink:to="lab_us-gaap_ProceedsFromLinesOfCredit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_019eb2fa-0349-7865-99cb-e81ce93af7af_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property and equipment, net of accumulated depreciation of $115,490 and $98,650 as of June&#160;30, 2026 and December&#160;31, 2025, respectively</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant, and Equipment and Finance Lease Right-of-Use Asset, after Accumulated Depreciation and Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentAndFinanceLeaseRightOfUseAssetAfterAccumulatedDepreciationAndAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_019eb2fa-03d6-793c-a296-22db12e29728_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DividendsShareBasedCompensation_019eb2fa-0349-799f-bc76-574b6874ace3_terseLabel_en-US" xlink:label="lab_us-gaap_DividendsShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment, dividend</link:label>
    <link:label id="lab_us-gaap_DividendsShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_DividendsShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividend, Share-Based Payment Arrangement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DividendsShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DividendsShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DividendsShareBasedCompensation" xlink:to="lab_us-gaap_DividendsShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_019eb2fa-03d6-7a66-9411-e886d06bcec1_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination_019eb2fa-0349-7d5f-8b14-29bc616071b2_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, Increase (Decrease) for Contract Acquired in Business Combination</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:to="lab_us-gaap_ContractWithCustomerAssetIncreaseDecreaseForContractAcquiredInBusinessCombination" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits_019eb2fa-0349-7d7f-b6a6-0885a9c81051_negatedTerseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and benefits</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability, Accrued Compensation And Benefits</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability, Accrued Compensation And Benefits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:to="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_019eb2fa-0349-7afd-87e7-5f04a3257f1b_terseLabel_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantor obligations, current carrying value</link:label>
    <link:label id="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue_label_en-US" xlink:label="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Guarantor Obligations, Current Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GuaranteeObligationsCurrentCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:to="lab_us-gaap_GuaranteeObligationsCurrentCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_019eb2fa-03d6-7bef-9776-30008ef15aa5_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_019eb2fa-0349-7dd6-a001-6a2c5445ea8f_terseLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerAbstract_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_019eb2fa-03d6-7eff-81d4-efe2fd2ec268_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other long-term assets and liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets and Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_019fda4a-e42d-7215-b16d-f8925d822263_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-lived asset impairment</link:label>
    <link:label id="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse_label_en-US" xlink:label="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Asset, Held and Used, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ImpairmentOfLongLivedAssetsHeldForUse"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:to="lab_us-gaap_ImpairmentOfLongLivedAssetsHeldForUse" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Goodwill and Other [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_019eb2fa-026d-7e13-b982-6bf2c7ecc9f2_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of credit outstanding</link:label>
    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_label_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Letters of Credit Outstanding, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LettersOfCreditOutstandingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LettersOfCreditOutstandingAmount" xlink:to="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019eb2fa-03d6-7a1c-ae87-a130cb418810_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation for RSUs and stock options</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_019eb2fa-026d-7396-8737-a52d14179cb8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeLiabilityAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019eb2fa-0349-7d48-a4ce-75e665b471d0_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_019eb2fa-0349-7700-97f3-ce8a60c117d2_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective income tax rate (as percent)</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_019eb2fa-03d6-7b3f-ab62-04560c1f9ed1_terseLabel_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of assumed exchange of LGN B Units (in shares)</link:label>
    <link:label id="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements_label_en-US" xlink:label="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable to Dilutive Effect of Share-Based Payment Arrangements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:to="lab_us-gaap_IncrementalCommonSharesAttributableToShareBasedPaymentArrangements" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_LegenceCorpMember_019eb2fa-0349-70a1-8bb3-c18a09c8d993_terseLabel_en-US" xlink:label="lab_lgn_LegenceCorpMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legence Corp</link:label>
    <link:label id="lab_lgn_LegenceCorpMember_label_en-US" xlink:label="lab_lgn_LegenceCorpMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legence Corp [Member]</link:label>
    <link:label id="lab_lgn_LegenceCorpMember_documentation_en-US" xlink:label="lab_lgn_LegenceCorpMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legence Corp</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_LegenceCorpMember" xlink:href="lgn-20260630.xsd#lgn_LegenceCorpMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_LegenceCorpMember" xlink:to="lab_lgn_LegenceCorpMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member_019eb2fa-0349-777e-9ec4-88a372b6b8eb_terseLabel_en-US" xlink:label="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3.4581% Interest Rate Swap, Maturing at December 2028</link:label>
    <link:label id="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member_label_en-US" xlink:label="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.4581% Interest Rate Swap, Maturing at December 2028 [Member]</link:label>
    <link:label id="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member_documentation_en-US" xlink:label="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.4581% Interest Rate Swap, Maturing at December 2028</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:href="lgn-20260630.xsd#lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:to="lab_lgn_A3.4581InterestRateSwapMaturingAtDecember2028Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_019eb2fa-03d6-7714-94c9-8156f4f5596c_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, current and long-term</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_PerformanceInterestsMember_019eb2fa-0349-722c-9e69-e66b0b644f62_terseLabel_en-US" xlink:label="lab_lgn_PerformanceInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Performance Interests</link:label>
    <link:label id="lab_lgn_PerformanceInterestsMember_label_en-US" xlink:label="lab_lgn_PerformanceInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Performance Interests [Member]</link:label>
    <link:label id="lab_lgn_PerformanceInterestsMember_documentation_en-US" xlink:label="lab_lgn_PerformanceInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Performance Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_PerformanceInterestsMember" xlink:href="lgn-20260630.xsd#lgn_PerformanceInterestsMember"/>
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    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_019eb2fa-026d-7735-9b49-cf97cf254986_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_019eb2fa-0349-754b-892d-34b7dbd18fe4_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets_019eb2fa-026d-729e-8565-55d874084bd7_terseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset, Operating Lease Right-of-use Assets</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Asset, Operating Lease Right-of-use Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:to="lab_lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019eb2fa-026d-7a94-a7c1-ce13ffde8b4d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use assets (including $18,598 and $20,025 as of June&#160;30, 2026 and December&#160;31, 2025, respectively, from related parties)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_019eb2fa-026d-789f-8beb-a1a02f1ccdf9_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:to="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ContributionsFromParentIIForSeriesAInterests_019eb2fa-03d6-76dc-b8ae-32c47816e308_terseLabel_en-US" xlink:label="lab_lgn_ContributionsFromParentIIForSeriesAInterests" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contribution from Legence Parent II for Series A Interests</link:label>
    <link:label id="lab_lgn_ContributionsFromParentIIForSeriesAInterests_label_en-US" xlink:label="lab_lgn_ContributionsFromParentIIForSeriesAInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contributions From Parent II For Series A Interests</link:label>
    <link:label id="lab_lgn_ContributionsFromParentIIForSeriesAInterests_documentation_en-US" xlink:label="lab_lgn_ContributionsFromParentIIForSeriesAInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contributions From Parent II For Series A Interests</link:label>
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    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_019eb2fa-0349-7b1e-bc0b-2def932a3000_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AOCI, Net of Tax [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Including Portion Attributable to Noncontrolling Interest, Net of Tax [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019eb2fa-0349-7727-8a56-dd6cef9ceee0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Computation of Basic and Diluted EPS</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_019eb2fa-03d6-7718-a31c-1f716210de78_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net acquired assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less), and Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNet"/>
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    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestLineItems_019eb2fa-026d-78ed-b692-074f084b1c0c_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Line Items]</link:label>
    <link:label id="lab_us-gaap_MinorityInterestLineItems_label_en-US" xlink:label="lab_us-gaap_MinorityInterestLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestLineItems" xlink:to="lab_us-gaap_MinorityInterestLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019eb2fa-03d6-7d2c-a654-14df48507942_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent_019eb2fa-03d6-7cd5-89db-01697c890502_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Current portion of long-term debt</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent_019eb2fa-03d6-7f44-a381-3edebc34cf6a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: Current portion</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligationsCurrent"/>
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    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_019eb2fa-0349-72c6-bf03-18c74e68c0f9_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Information</link:label>
    <link:label id="lab_us-gaap_SegmentReportingDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SegmentReportingDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingDisclosureTextBlock" xlink:to="lab_us-gaap_SegmentReportingDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_019eb2fa-0349-7c8b-8588-b2603fb99733_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
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    <link:label id="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember_019eb2fa-026d-7fb6-a01e-2b81ce2b62b4_terseLabel_en-US" xlink:label="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred consideration related to Bowers acquisition</link:label>
    <link:label id="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember_label_en-US" xlink:label="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Consideration Related To Acquisition [Member]</link:label>
    <link:label id="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember_documentation_en-US" xlink:label="lab_lgn_DeferredConsiderationRelatedToAcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Consideration Related To Acquisition</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_019eb2fa-0349-777a-a46d-aab839bf32b6_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Axis]</link:label>
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    <link:label id="lab_us-gaap_StatementOfIncomeLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Income, Balance [Axis]</link:label>
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    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
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    <link:label id="lab_lgn_InstallationAndFabricationMember_label_en-US" xlink:label="lab_lgn_InstallationAndFabricationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Installation And Fabrication [Member]</link:label>
    <link:label id="lab_lgn_InstallationAndFabricationMember_documentation_en-US" xlink:label="lab_lgn_InstallationAndFabricationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Installation And Fabrication</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_InstallationAndFabricationMember" xlink:href="lgn-20260630.xsd#lgn_InstallationAndFabricationMember"/>
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    <link:label id="lab_us-gaap_InterestRateSwapMember_019eb2fa-03d6-71d1-a107-4606ac28bad2_terseLabel_en-US" xlink:label="lab_us-gaap_InterestRateSwapMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap instruments</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureTextBlock" xlink:to="lab_us-gaap_DebtDisclosureTextBlock" xlink:type="arc" order="1"/>
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    <link:label id="lab_lgn_EngineeringAndConsultingMember_label_en-US" xlink:label="lab_lgn_EngineeringAndConsultingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Engineering And Consulting [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent_019eb2fa-03d6-7d9c-afbe-a62f344139d5_terseLabel_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A Common Stock for acquisitions</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent_label_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions, Percent</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent_documentation_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:href="lgn-20260630.xsd#lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:to="lab_lgn_StockIssuedDuringPeriodSharesAcquisitionsPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019eb2fa-03d6-755e-848b-c91e4e57fc7f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stated interest rate (as percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_019eb2fa-0349-7c39-a41e-531ccffb9a40_terseLabel_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:label id="lab_srt_RepurchaseAgreementCounterpartyNameDomain_label_en-US" xlink:label="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RepurchaseAgreementCounterpartyNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:to="lab_srt_RepurchaseAgreementCounterpartyNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019eb2fa-026d-7488-a1a7-204beaa498f9_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total Legence stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_019eb2fa-026e-74b3-8e31-eaca0a30c76f_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total other expense, net</link:label>
    <link:label id="lab_us-gaap_NonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_NonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonoperatingIncomeExpense" xlink:to="lab_us-gaap_NonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_019eb2fa-03d6-7654-9983-95d773d92f90_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Other Asset, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherNoncurrentAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_019eb2fa-026d-7397-8174-1baf1b731743_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019eb2fa-026d-7f2f-8ffe-d8cd7e05826e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of issued (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:to="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFeeAmount_019eb2fa-0349-7f4a-8021-e4a0c0691320_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fees incurred from third parties</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFeeAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fee Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFeeAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFeeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFeeAmount" xlink:to="lab_us-gaap_DebtInstrumentFeeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_019eb2fa-03d6-7ea2-ba34-d55465a124c2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Payments for deferred offering costs</link:label>
    <link:label id="lab_us-gaap_PaymentsOfStockIssuanceCosts_label_en-US" xlink:label="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments of Stock Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsOfStockIssuanceCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfStockIssuanceCosts" xlink:to="lab_us-gaap_PaymentsOfStockIssuanceCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_019eb2fa-0349-72d5-84f1-7e2acf8f4a11_verboseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_FinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finance Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeaseLiability" xlink:to="lab_us-gaap_FinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_019eb2fa-026d-7ec6-b386-903b562ca029_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement period adjustments</link:label>
    <link:label id="lab_us-gaap_GoodwillPurchaseAccountingAdjustments_label_en-US" xlink:label="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Measurement Period Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillPurchaseAccountingAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:to="lab_us-gaap_GoodwillPurchaseAccountingAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_019ff43f-3ca9-70ae-944a-e633248fbeff_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities_label_en-US" xlink:label="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from (Payment for) Other Financing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromPaymentsForOtherFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:to="lab_us-gaap_ProceedsFromPaymentsForOtherFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Adopted</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcAdoptedFlag"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019eb2fa-03d6-7517-84af-0a9fa5c55cab_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash provided by operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest_019fcb6d-4930-781c-be19-553ade91f749_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_019eb2fa-0349-73d3-a59f-6e070766d90b_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, remaining performance obligation (as percent)</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligationPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligationPercentage"/>
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    <link:label id="lab_lgn_EngineeringAndDesignMember_019eb2fa-0349-7713-a99a-6e7d00094c23_terseLabel_en-US" xlink:label="lab_lgn_EngineeringAndDesignMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Engineering &amp; Design</link:label>
    <link:label id="lab_lgn_EngineeringAndDesignMember_label_en-US" xlink:label="lab_lgn_EngineeringAndDesignMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Engineering And Design [Member]</link:label>
    <link:label id="lab_lgn_EngineeringAndDesignMember_documentation_en-US" xlink:label="lab_lgn_EngineeringAndDesignMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Engineering And Design</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_EngineeringAndDesignMember" xlink:href="lgn-20260630.xsd#lgn_EngineeringAndDesignMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_EngineeringAndDesignMember" xlink:to="lab_lgn_EngineeringAndDesignMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_019eb2fa-0349-7a43-930d-de868e4589ab_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized gain (loss) recognized in AOCI</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Reclassifications, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_019eb2fa-03d6-7ce2-840e-aaf5e60451dd_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders' equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityAbstract" xlink:to="lab_us-gaap_StockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_019eb2fa-026d-7da8-be89-d0ebb12da459_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipAxis_019eb2fa-03d6-7a2d-ba68-3b279b337d38_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipAxis" xlink:to="lab_srt_OwnershipAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019eb2fa-03d6-738a-ba27-b9a0d18e085b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee_019eb2fa-0349-73e8-8ef0-c60889581099_terseLabel_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum annual cash payments</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee_label_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Value During Offering Period, Per Employee</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee_documentation_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Value During Offering Period, Per Employee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:href="lgn-20260630.xsd#lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:to="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_019eb2fa-03d6-7c79-b655-6b78ec245ce8_terseLabel_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument</link:label>
    <link:label id="lab_us-gaap_DesignatedAsHedgingInstrumentMember_label_en-US" xlink:label="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Designated as Hedging Instrument [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DesignatedAsHedgingInstrumentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:to="lab_us-gaap_DesignatedAsHedgingInstrumentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember_019eb2fa-0349-7f7e-a44f-2f1bc87c7636_terseLabel_en-US" xlink:label="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Promissory Note Payable In Connection With 2024 And 2022 Acquisition</link:label>
    <link:label id="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember_label_en-US" xlink:label="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Promissory Note Payable In Connection With 2024 And 2022 Acquisition [Member]</link:label>
    <link:label id="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember_documentation_en-US" xlink:label="lab_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Promissory Note Payable In Connection With 2024 And 2022 Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember" xlink:href="lgn-20260630.xsd#lgn_PromissoryNotePayableInConnectionWith2024And2022AcquisitionMember"/>
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    <link:label id="lab_us-gaap_OperatingExpensesAbstract_019eb2fa-0349-7a1f-a3ef-daac23bc6c2e_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_019eb2fa-0349-7409-9d0e-4c8f1441da56_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred income tax assets, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxAssetsNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Assets, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxAssetsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxAssetsNet" xlink:to="lab_us-gaap_DeferredIncomeTaxAssetsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_terseLabel_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs)</link:label>
    <link:label id="lab_us-gaap_StockAppreciationRightsSARSMember_label_en-US" xlink:label="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Appreciation Rights (SARs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockAppreciationRightsSARSMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockAppreciationRightsSARSMember" xlink:to="lab_us-gaap_StockAppreciationRightsSARSMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_019eb2fa-026d-71a3-9c92-57e6e169de40_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reduction to interest rate (as percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateIncreaseDecrease" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentInterestRateIncreaseDecrease"/>
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    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_019eb2fa-0349-7cce-84f3-a8ea7cead3bf_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Identifiable Intangible Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFiniteLivedIntangibleAssetsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019eb2fa-03d6-7111-8de6-059a6ca230a8_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, basis spread on variable rate (as percent)</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019eb2fa-03d6-7546-a4c5-1283a3ea3c9f_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateDomain_019eb2fa-0349-7a99-824e-3f344e39f6d6_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:label id="lab_us-gaap_VariableRateDomain_label_en-US" xlink:label="lab_us-gaap_VariableRateDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateDomain" xlink:to="lab_us-gaap_VariableRateDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019ec9cb-9724-7787-9d1c-0a41ca1f5fb6_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss)</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_019eb2fa-026d-712e-9345-4b5fe79b476b_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease right-of-use asset lease expense</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_019eb2fa-026d-7b3b-a42e-e7fd3a414575_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total debt</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFairValue_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFairValue" xlink:to="lab_us-gaap_DebtInstrumentFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_MetrixEngineersLLCMember_019eb2fa-026d-73a9-80e7-8963f2122a57_terseLabel_en-US" xlink:label="lab_lgn_MetrixEngineersLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Metrix</link:label>
    <link:label id="lab_lgn_MetrixEngineersLLCMember_label_en-US" xlink:label="lab_lgn_MetrixEngineersLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Metrix Engineers, LLC [Member]</link:label>
    <link:label id="lab_lgn_MetrixEngineersLLCMember_documentation_en-US" xlink:label="lab_lgn_MetrixEngineersLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Metrix Engineers, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_MetrixEngineersLLCMember" xlink:href="lgn-20260630.xsd#lgn_MetrixEngineersLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_MetrixEngineersLLCMember" xlink:to="lab_lgn_MetrixEngineersLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityListingsTable_019eb2fa-026d-7db9-9d8c-f4c16a6b9da4_terseLabel_en-US" xlink:label="lab_dei_EntityListingsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Listings [Table]</link:label>
    <link:label id="lab_dei_EntityListingsTable_label_en-US" xlink:label="lab_dei_EntityListingsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Listings [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityListingsTable" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityListingsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityListingsTable" xlink:to="lab_dei_EntityListingsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_019eb2fa-026d-78ee-9354-d13e9ff221b6_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected life (years)</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description</link:label>
    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonGaapMeasureDescriptionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonGaapMeasureDescriptionTextBlock" xlink:to="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_019eb2fa-0349-7d78-9eb9-4c281c1ba331_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Legence Corp. Class A Common Stock</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsNoncurrent_019eb2fa-0349-7dd2-a595-374aaffbf267_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_AssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_AssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsNoncurrent" xlink:to="lab_us-gaap_AssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019eb2fa-0349-72fd-8ae6-a4007798e4d0_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_019eb2fa-026d-7c64-a565-89df103004be_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_019eb2fa-026d-7b68-b736-1041755c074f_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonUnitOutstanding_019eb2fa-0349-7e57-b1dd-15dc1984b00c_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonUnitOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Common unit, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonUnitOutstanding_019eb2fa-0349-7221-a362-3e9cb4e850a1_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonUnitOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Common unit, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonUnitOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonUnitOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Unit, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonUnitOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonUnitOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonUnitOutstanding" xlink:to="lab_us-gaap_CommonUnitOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019eb2fa-0349-7dd2-b636-181a4959ff9e_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_SecondaryOfferingMember_019eb2fa-0349-70da-bc37-677e154da722_terseLabel_en-US" xlink:label="lab_lgn_SecondaryOfferingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secondary Offering</link:label>
    <link:label id="lab_lgn_SecondaryOfferingMember_label_en-US" xlink:label="lab_lgn_SecondaryOfferingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secondary Offering [Member]</link:label>
    <link:label id="lab_lgn_SecondaryOfferingMember_documentation_en-US" xlink:label="lab_lgn_SecondaryOfferingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Secondary Offering</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_SecondaryOfferingMember" xlink:href="lgn-20260630.xsd#lgn_SecondaryOfferingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_SecondaryOfferingMember" xlink:to="lab_lgn_SecondaryOfferingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_019eb2fa-03d6-79bb-820e-36f7176c1d0e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_019eb2fa-03d6-700e-8296-77dfb99aa365_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reservation of shares (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets_019eb2fa-03d6-795a-991d-487046d5053b_terseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract assets</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Contract Assets</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Contract Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:to="lab_lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_019eb2fa-026d-76d8-82b7-dbe8bc4e5169_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest expense</link:label>
    <link:label id="lab_us-gaap_InterestExpenseNonoperating_label_en-US" xlink:label="lab_us-gaap_InterestExpenseNonoperating" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Nonoperating</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseNonoperating" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestExpenseNonoperating"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseNonoperating" xlink:to="lab_us-gaap_InterestExpenseNonoperating" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_019eb2fa-03d6-7d6e-8461-58ba77fba1f9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Compensation Expense And Corresponding Income Tax Benefit</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:to="lab_us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_GoodwillReportingUnitImpairedNumber_019ff0e6-8836-7cd1-91d3-eedb161d4804_terseLabel_en-US" xlink:label="lab_lgn_GoodwillReportingUnitImpairedNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reporting unit, impaired</link:label>
    <link:label id="lab_lgn_GoodwillReportingUnitImpairedNumber_label_en-US" xlink:label="lab_lgn_GoodwillReportingUnitImpairedNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Reporting Unit, Impaired, Number</link:label>
    <link:label id="lab_lgn_GoodwillReportingUnitImpairedNumber_documentation_en-US" xlink:label="lab_lgn_GoodwillReportingUnitImpairedNumber" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Goodwill, Reporting Unit, Impaired, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_GoodwillReportingUnitImpairedNumber" xlink:href="lgn-20260630.xsd#lgn_GoodwillReportingUnitImpairedNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_GoodwillReportingUnitImpairedNumber" xlink:to="lab_lgn_GoodwillReportingUnitImpairedNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_019eb2fa-03d6-7cf9-aa9a-4350ca7ce425_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_019eb2fa-026d-7dee-a9ef-94ca15c59d87_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-Based Compensation and Long-term Incentive Awards</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_019eb2fa-0349-71e7-a0ac-94933178d69b_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Domain]</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_Other2025AcquisitionMember_019eb2fa-026d-71f6-a420-4eff52b35f44_terseLabel_en-US" xlink:label="lab_lgn_Other2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other 2025 Acquisition</link:label>
    <link:label id="lab_lgn_Other2025AcquisitionMember_label_en-US" xlink:label="lab_lgn_Other2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other 2025 Acquisition [Member]</link:label>
    <link:label id="lab_lgn_Other2025AcquisitionMember_documentation_en-US" xlink:label="lab_lgn_Other2025AcquisitionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other 2025 Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_Other2025AcquisitionMember" xlink:href="lgn-20260630.xsd#lgn_Other2025AcquisitionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_Other2025AcquisitionMember" xlink:to="lab_lgn_Other2025AcquisitionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_019eb2fa-0349-7da7-af6b-b2b06952a1ab_terseLabel_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation expense</link:label>
    <link:label id="lab_us-gaap_AllocatedShareBasedCompensationExpense_label_en-US" xlink:label="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AllocatedShareBasedCompensationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AllocatedShareBasedCompensationExpense" xlink:to="lab_us-gaap_AllocatedShareBasedCompensationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate_019eb2fa-0349-74f2-9c99-e05281af4dc8_terseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional basis spread on variable rate</link:label>
    <link:label id="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate_label_en-US" xlink:label="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Additional Basis Spread On Variable Rate</link:label>
    <link:label id="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Additional Basis Spread On Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:to="lab_lgn_DebtInstrumentAdditionalBasisSpreadOnVariableRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019eb2fa-0349-7f06-a06c-8f189e2725c7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_019eb2fa-026d-7600-9329-1a54c3b4df6e_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other long-term liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherLiabilitiesNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesNoncurrent" xlink:to="lab_us-gaap_OtherLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Goodwill_019eb2fa-026d-7c07-ab41-02bf859c0e66_terseLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:label id="lab_us-gaap_Goodwill_019eb2fa-026d-77eb-ac9d-12ef0f7c896b_periodStartLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Beginning Balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_019eb2fa-026d-73c5-b266-393202d5096d_periodEndLabel_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Goodwill, Ending Balance</link:label>
    <link:label id="lab_us-gaap_Goodwill_label_en-US" xlink:label="lab_us-gaap_Goodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Goodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Goodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Goodwill" xlink:to="lab_us-gaap_Goodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent_019eb2fa-026d-73cb-834a-5d7288ff0809_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax receivable agreement liability - related party</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Noncurrent</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:to="lab_lgn_TaxReceivableAgreementLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_019eb2fa-03d6-72a3-82d0-1b968d374c19_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions</link:label>
    <link:label id="lab_us-gaap_GoodwillAcquiredDuringPeriod_label_en-US" xlink:label="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Acquired During Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAcquiredDuringPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAcquiredDuringPeriod" xlink:to="lab_us-gaap_GoodwillAcquiredDuringPeriod" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_019eb2fa-0349-70c2-ad10-733d3869e095_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liability revenue recognized during the period</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Revenue Recognized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityRevenueRecognized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityRevenueRecognized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_019eb2fa-0349-7c02-9f91-d17eb03ebfa1_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_019fe92c-7e2e-7bda-a712-bbd5ba509bb0_terseLabel_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax payable</link:label>
    <link:label id="lab_us-gaap_TaxesPayableCurrent_label_en-US" xlink:label="lab_us-gaap_TaxesPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Taxes Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TaxesPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TaxesPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TaxesPayableCurrent" xlink:to="lab_us-gaap_TaxesPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_019eb2fa-0349-7a3c-b214-f38d77f3b22d_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities, net of current portion (including $15,759 and $17,282 as of June&#160;30, 2026 and December&#160;31, 2025, respectively, from related parties)</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingLeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:to="lab_us-gaap_OperatingLeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability_019eb2fa-0349-79ef-af06-0d64c023a839_negatedTerseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Contract Liability</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Contract Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:to="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_019eb2fa-03d6-7bbd-849e-00fc820bfd3c_terseLabel_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Money Market Funds</link:label>
    <link:label id="lab_us-gaap_MoneyMarketFundsMember_label_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Money Market Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MoneyMarketFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MoneyMarketFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MoneyMarketFundsMember" xlink:to="lab_us-gaap_MoneyMarketFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_019eb2fa-03d6-7ea5-a796-9ccaea492baf_terseLabel_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility</link:label>
    <link:label id="lab_us-gaap_RevolvingCreditFacilityMember_label_en-US" xlink:label="lab_us-gaap_RevolvingCreditFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revolving Credit Facility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevolvingCreditFacilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevolvingCreditFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevolvingCreditFacilityMember" xlink:to="lab_us-gaap_RevolvingCreditFacilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_019eb2fa-03d6-7f34-a520-44195ef2c4d7_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_019eb2fa-0349-713e-9819-96ddc6026d56_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019eb2fa-03d6-7698-9524-b0a4a7dd84d1_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019eb2fa-03d6-7422-b006-db1ac5c681e9_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019eb2fa-03d6-7c28-a06b-1c60f9dd2e97_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgDiscLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgDiscLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgDiscLineItems" xlink:to="lab_ecd_AwardTmgDiscLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019eb2fa-03d6-749c-bab4-6cc2ee41d8b8_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019eb2fa-03d6-7b5f-b0aa-e5cebaffe3ec_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Loss per share&#8212;diluted (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019eb2fa-0349-7796-a1b2-6554bd253189_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019eb2fa-026d-7e53-8516-eae83661d27f_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash provided by (used in) financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent_019fcb67-2f71-7426-9a47-78be2eeb1c71_terseLabel_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A Common Stock for vested RSUs (as percent)</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent_label_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Restricted Stock Award, Net of Forfeitures, Percent</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent_documentation_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Restricted Stock Award, Net of Forfeitures, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:href="lgn-20260630.xsd#lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:to="lab_lgn_StockIssuedDuringPeriodSharesRestrictedStockAwardNetOfForfeituresPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_019eb2fa-026d-75ff-a692-71f93583cc0e_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses and other current assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_019eb2fa-03d6-7455-9efb-788ea17c4a49_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging</link:label>
    <link:label id="lab_us-gaap_CashFlowHedgingMember_label_en-US" xlink:label="lab_us-gaap_CashFlowHedgingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Flow Hedging [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowHedgingMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashFlowHedgingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowHedgingMember" xlink:to="lab_us-gaap_CashFlowHedgingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_LegenceHoldingsLLCMember_019eb2fa-026d-7822-919d-127bbe323973_terseLabel_en-US" xlink:label="lab_lgn_LegenceHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legence Holdings LLC</link:label>
    <link:label id="lab_lgn_LegenceHoldingsLLCMember_label_en-US" xlink:label="lab_lgn_LegenceHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legence Holdings LLC [Member]</link:label>
    <link:label id="lab_lgn_LegenceHoldingsLLCMember_documentation_en-US" xlink:label="lab_lgn_LegenceHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legence Holdings LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_LegenceHoldingsLLCMember" xlink:href="lgn-20260630.xsd#lgn_LegenceHoldingsLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_LegenceHoldingsLLCMember" xlink:to="lab_lgn_LegenceHoldingsLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities_019eb2fa-026d-736e-a48d-a6c6e6b94214_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation and benefits</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Employee Related Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInEmployeeRelatedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_InstallationMaintenanceMember_019eb2fa-0349-7eb9-994d-59947601f07c_terseLabel_en-US" xlink:label="lab_lgn_InstallationMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Installation &amp; Maintenance</link:label>
    <link:label id="lab_lgn_InstallationMaintenanceMember_label_en-US" xlink:label="lab_lgn_InstallationMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Installation &amp; Maintenance [Member]</link:label>
    <link:label id="lab_lgn_InstallationMaintenanceMember_documentation_en-US" xlink:label="lab_lgn_InstallationMaintenanceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Installation &amp; Maintenance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_InstallationMaintenanceMember" xlink:href="lgn-20260630.xsd#lgn_InstallationMaintenanceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_InstallationMaintenanceMember" xlink:to="lab_lgn_InstallationMaintenanceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_019eb2fa-026d-75da-85c9-22f690818f37_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization of intangible assets</link:label>
    <link:label id="lab_us-gaap_AmortizationOfIntangibleAssets_label_en-US" xlink:label="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AmortizationOfIntangibleAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfIntangibleAssets" xlink:to="lab_us-gaap_AmortizationOfIntangibleAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable_019eb2fa-0349-74a2-ad44-7f515258fc66_terseLabel_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred offering costs included in Accounts payable</link:label>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable_label_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs Included In Accounts Payable</link:label>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable_documentation_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs Included In Accounts Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:href="lgn-20260630.xsd#lgn_DeferredOfferingCostsIncludedInAccountsPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:to="lab_lgn_DeferredOfferingCostsIncludedInAccountsPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_019eb2fa-03d6-7299-83fc-b66e493f5dae_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Consideration Transferred</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019eb2fa-0349-7abc-8fd7-e749638528c0_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges_019eb2fa-0349-719a-9547-a797733d8741_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tax receivable agreement liability and deferred taxes arising from exchanges of Class B Common Stock</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Secondary Offering Exchanges</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement Liability, Secondary Offering Exchanges</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:to="lab_lgn_TaxReceivableAgreementLiabilitySecondaryOfferingExchanges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_019eb2fa-026d-7a8b-a7f8-ab1abf0ea29b_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Supplemental Pro Forma Information</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionProFormaInformationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019eb2fa-0349-79c9-bb36-fecf19169882_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to cash provided by operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_019eb2fa-026d-7097-a2c0-ccc90ff0099c_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis_label_en-US" xlink:label="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency Nature [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingenciesByNatureOfContingencyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:to="lab_us-gaap_LossContingenciesByNatureOfContingencyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TheBowersGroupInc.Member_019eb2fa-026d-7aac-8b74-e5242379f434_terseLabel_en-US" xlink:label="lab_lgn_TheBowersGroupInc.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Bowers</link:label>
    <link:label id="lab_lgn_TheBowersGroupInc.Member_label_en-US" xlink:label="lab_lgn_TheBowersGroupInc.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">The Bowers Group, Inc. [Member]</link:label>
    <link:label id="lab_lgn_TheBowersGroupInc.Member_documentation_en-US" xlink:label="lab_lgn_TheBowersGroupInc.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">The Bowers Group, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TheBowersGroupInc.Member" xlink:href="lgn-20260630.xsd#lgn_TheBowersGroupInc.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TheBowersGroupInc.Member" xlink:to="lab_lgn_TheBowersGroupInc.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NonrecurringAdjustmentDomain_019eb2fa-026d-70c5-9e49-a948cc866470_terseLabel_en-US" xlink:label="lab_us-gaap_NonrecurringAdjustmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment [Domain]</link:label>
    <link:label id="lab_us-gaap_NonrecurringAdjustmentDomain_label_en-US" xlink:label="lab_us-gaap_NonrecurringAdjustmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NonrecurringAdjustmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NonrecurringAdjustmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NonrecurringAdjustmentDomain" xlink:to="lab_us-gaap_NonrecurringAdjustmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019eb2fa-03d6-7f89-8312-3ca7f9e84189_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_019eb2fa-0349-7ec4-9bbd-aa4eef19d0fc_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_019eb2fa-0349-7643-b07d-042a3d9e8297_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Available for borrowing under revolving line of credit</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Remaining Borrowing Capacity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:to="lab_us-gaap_LineOfCreditFacilityRemainingBorrowingCapacity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_019eb2fa-03d6-70b1-85ff-abc73fcac2b3_terseLabel_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Line of credit facility, unused capacity, commitment fee (as percent)</link:label>
    <link:label id="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage_label_en-US" xlink:label="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line of Credit Facility, Unused Capacity, Commitment Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:to="lab_us-gaap_LineOfCreditFacilityUnusedCapacityCommitmentFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_RestrictedSeriesCInterestsMember_019eb2fa-0349-783e-9647-24e463f31e5c_terseLabel_en-US" xlink:label="lab_lgn_RestrictedSeriesCInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Series C Common Interests</link:label>
    <link:label id="lab_lgn_RestrictedSeriesCInterestsMember_label_en-US" xlink:label="lab_lgn_RestrictedSeriesCInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Series C Interests [Member]</link:label>
    <link:label id="lab_lgn_RestrictedSeriesCInterestsMember_documentation_en-US" xlink:label="lab_lgn_RestrictedSeriesCInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Series C Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_RestrictedSeriesCInterestsMember" xlink:href="lgn-20260630.xsd#lgn_RestrictedSeriesCInterestsMember"/>
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    <link:label id="lab_lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member_label_en-US" xlink:label="lab_lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.6995% Interest Rate Swap, Maturing at December 2028 [Member]</link:label>
    <link:label id="lab_lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member_documentation_en-US" xlink:label="lab_lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.6995% Interest Rate Swap, Maturing at December 2028</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member" xlink:href="lgn-20260630.xsd#lgn_A3.6995InterestRateSwapMaturingAtDecember2028Member"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_019eb2fa-03d6-7948-9585-c361dcbc7e74_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator&#8212;basic:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
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    <link:label id="lab_us-gaap_DerivativeAssets_019eb2fa-03d6-7e33-9e33-45264242cf6b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeAssets_label_en-US" xlink:label="lab_us-gaap_DerivativeAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssets" xlink:to="lab_us-gaap_DerivativeAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_019eb2fa-0349-781d-b6eb-5ccee357d1df_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
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    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_019eb2fa-026d-762f-90cb-ca6db63d4ba1_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets</link:label>
    <link:label id="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset and Goodwill [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_terseLabel_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Securities</link:label>
    <link:label id="lab_ecd_AwardUndrlygSecuritiesAmt_label_en-US" xlink:label="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Underlying Securities Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardUndrlygSecuritiesAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardUndrlygSecuritiesAmt" xlink:to="lab_ecd_AwardUndrlygSecuritiesAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_019eb2fa-03d6-715f-b2db-167899475b39_terseLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Comprehensive (loss) income attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019eb2fa-0349-769e-a81d-714f29aa8cdf_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_019eb2fa-0349-71e6-a34a-52e56e9835d3_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue Recognition and Related Balance Sheet Accounts</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from Contract with Customer [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueFromContractWithCustomerTextBlock"/>
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    <link:label id="lab_lgn_PhilippeLeBrisMember_label_en-US" xlink:label="lab_lgn_PhilippeLeBrisMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Philippe Le Bris [Member]</link:label>
    <link:label id="lab_lgn_PhilippeLeBrisMember_documentation_en-US" xlink:label="lab_lgn_PhilippeLeBrisMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Philippe Le Bris</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_PhilippeLeBrisMember" xlink:href="lgn-20260630.xsd#lgn_PhilippeLeBrisMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_PhilippeLeBrisMember" xlink:to="lab_lgn_PhilippeLeBrisMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OverAllotmentOptionMember_019eb2fa-026d-7673-b294-314d87d35a69_terseLabel_en-US" xlink:label="lab_us-gaap_OverAllotmentOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Over-Allotment Option</link:label>
    <link:label id="lab_us-gaap_OverAllotmentOptionMember_label_en-US" xlink:label="lab_us-gaap_OverAllotmentOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Over-Allotment Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OverAllotmentOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OverAllotmentOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OverAllotmentOptionMember" xlink:to="lab_us-gaap_OverAllotmentOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_019eb2fa-0349-7fd3-b202-02c8694ffc9e_terseLabel_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prepaid expenses</link:label>
    <link:label id="lab_us-gaap_PrepaidExpenseCurrent_label_en-US" xlink:label="lab_us-gaap_PrepaidExpenseCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prepaid Expense, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrepaidExpenseCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PrepaidExpenseCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrepaidExpenseCurrent" xlink:to="lab_us-gaap_PrepaidExpenseCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock_019eb2fa-03d6-7ac4-9500-ff794c9e09c9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash Flow Hedges Included in Accumulated Other Comprehensive Income</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfCashFlowHedgesIncludedInAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
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    <link:label id="lab_us-gaap_Cash_019eb2fa-03d6-780e-8394-082b99206718_terseLabel_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_Cash_label_en-US" xlink:label="lab_us-gaap_Cash" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Cash" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_Cash"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_019eb2fa-026d-77e1-9bfb-1fb7aa501747_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A Common Stock for acquisitions (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesAcquisitions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesAcquisitions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_019eb2fa-0349-7123-8bad-f69504bf1b32_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal payments on term loans</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Periodic Payment, Principal</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentPeriodicPaymentPrincipal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:to="lab_us-gaap_DebtInstrumentPeriodicPaymentPrincipal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019eb2fa-0349-7b5e-b3b3-1e2be34eff7d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate_019eb2fa-03d6-7c4e-9c9c-738ab0c9041d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Eligible employees contribution percentage</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Maximum Employee Subscription Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019eb2fa-0349-79a6-b49e-1118e31e4b14_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_019eb2fa-026d-72af-879f-755bd13161b3_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:to="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_019eb2fa-0349-7f9e-a077-c4266a344e4b_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquiree's revenue since acquisition date</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Revenue since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:to="lab_us-gaap_BusinessCombinationProFormaInformationRevenueOfAcquireeSinceAcquisitionDateActual" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_019eb2fa-0349-79b4-8a0d-b19c37548059_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">(Loss) income from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_019eb2fa-026d-7e88-b69c-bc82d92a30ec_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue, remaining performance obligation</link:label>
    <link:label id="lab_us-gaap_RevenueRemainingPerformanceObligation_label_en-US" xlink:label="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue, Remaining Performance Obligation, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RevenueRemainingPerformanceObligation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueRemainingPerformanceObligation" xlink:to="lab_us-gaap_RevenueRemainingPerformanceObligation" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019eb2fa-03d6-7c18-a144-50198f690911_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019eb2fa-03d6-7d58-9f43-e35c36f01d5e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisitions</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ProfessionalCorporationsMember_019eb2fa-0349-758a-9c77-75fa0c6ed7d8_terseLabel_en-US" xlink:label="lab_lgn_ProfessionalCorporationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Professional Corporations</link:label>
    <link:label id="lab_lgn_ProfessionalCorporationsMember_label_en-US" xlink:label="lab_lgn_ProfessionalCorporationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Professional Corporations [Member]</link:label>
    <link:label id="lab_lgn_ProfessionalCorporationsMember_documentation_en-US" xlink:label="lab_lgn_ProfessionalCorporationsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Professional Corporations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ProfessionalCorporationsMember" xlink:href="lgn-20260630.xsd#lgn_ProfessionalCorporationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ProfessionalCorporationsMember" xlink:to="lab_lgn_ProfessionalCorporationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019eb2fa-0349-7154-a660-326c6c050f34_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCostsCurrent_019eb2fa-026d-760d-a0b0-f64ef312885e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred contract costs</link:label>
    <link:label id="lab_us-gaap_DeferredCostsCurrent_label_en-US" xlink:label="lab_us-gaap_DeferredCostsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Costs, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCostsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCostsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCostsCurrent" xlink:to="lab_us-gaap_DeferredCostsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RecoveryOfErrCompDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:to="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_019eb2fa-026d-7716-a292-35e0f6cd543b_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019eb2fa-0349-7bc8-9d78-1a5a79ca921d_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_019eb2fa-0349-7af6-9218-2947898e283f_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entities and Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_019eb2fa-03d6-7cd5-9d8a-01827851b586_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Amounts and Classification of the PCs' Assets and Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ExitInterestsMember_019eb2fa-03d6-710d-98a1-6e5353ffc3ed_terseLabel_en-US" xlink:label="lab_lgn_ExitInterestsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit Interests</link:label>
    <link:label id="lab_lgn_ExitInterestsMember_label_en-US" xlink:label="lab_lgn_ExitInterestsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Exit Interests [Member]</link:label>
    <link:label id="lab_lgn_ExitInterestsMember_documentation_en-US" xlink:label="lab_lgn_ExitInterestsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Exit Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ExitInterestsMember" xlink:href="lgn-20260630.xsd#lgn_ExitInterestsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ExitInterestsMember" xlink:to="lab_lgn_ExitInterestsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII_019eb2fa-0349-7a45-9422-90343ec9f082_terseLabel_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contribution from Legence Parent II for Series A Interests</link:label>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII_label_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid In Capital, Contributions From Parent II</link:label>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII_documentation_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid In Capital, Contributions From Parent II</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:href="lgn-20260630.xsd#lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:to="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentII" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent_019eb2fa-0349-7af6-a900-752a699794fc_negatedTerseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current portion of operating lease liabilities</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent_label_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Operating Lease Liabilities, Current</link:label>
    <link:label id="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Operating Lease Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:to="lab_lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019eb2fa-0349-710c-8165-0e1b3b33b390_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_019eb2fa-0349-7207-8b87-a602ad799e89_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductsAndServicesDomain_019eb2fa-03d6-7f25-a5d6-1a0bc499f0bf_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyMember_019eb2fa-0349-76d4-b27a-d7fb1feb93cc_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party</link:label>
    <link:label id="lab_us-gaap_RelatedPartyMember_label_en-US" xlink:label="lab_us-gaap_RelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyMember" xlink:to="lab_us-gaap_RelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019eb2fa-03d6-7888-a19d-6ebed551a67f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income taxes paid, net of refunds</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_019eb2fa-03d6-7c3b-93cc-fe776dbfbea7_terseLabel_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:label id="lab_us-gaap_DisaggregationOfRevenueTable_label_en-US" xlink:label="lab_us-gaap_DisaggregationOfRevenueTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disaggregation of Revenue [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisaggregationOfRevenueTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DisaggregationOfRevenueTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisaggregationOfRevenueTable" xlink:to="lab_us-gaap_DisaggregationOfRevenueTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonClassAMember_019eb2fa-03d6-72c3-88e1-7505037b4f79_terseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Class A</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_019eb2fa-03d6-74ba-975a-739573ebd9c3_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Class A Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonClassAMember_label_en-US" xlink:label="lab_us-gaap_CommonClassAMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Class A [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonClassAMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonClassAMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonClassAMember" xlink:to="lab_us-gaap_CommonClassAMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019eb2fa-03d6-7e00-ba8f-dcbef87ed08d_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableRateAxis_019eb2fa-0349-7768-92d9-bf0063387ff2_terseLabel_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:label id="lab_us-gaap_VariableRateAxis_label_en-US" xlink:label="lab_us-gaap_VariableRateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Rate [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableRateAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableRateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableRateAxis" xlink:to="lab_us-gaap_VariableRateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_019eb2fa-0349-7d3a-a88c-ed3ab1d4eb84_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquiree's earnings (loss) since acquisition date</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquiree's Earnings (Loss) since Acquisition Date, Actual</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationProFormaInformationEarningsOrLossOfAcquireeSinceAcquisitionDateActual"/>
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    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_019eb2fa-0349-7062-9f95-64d37f593b0b_netLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Less: Net loss attributable to noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLossAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_NetIncomeLossAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent_019ff775-49d8-7c64-b2da-e99fffdbd786_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued compensation</link:label>
    <link:label id="lab_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Compensation Liability, Current and Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent" xlink:to="lab_us-gaap_DeferredCompensationLiabilityCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions_019eb2fa-026d-75b5-8502-463f4a7daf4f_terseLabel_en-US" xlink:label="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract asset, retentions</link:label>
    <link:label id="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions_label_en-US" xlink:label="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Retentions</link:label>
    <link:label id="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions_documentation_en-US" xlink:label="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contract with Customer, Asset, after Allowance for Credit Loss, Retentions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:href="lgn-20260630.xsd#lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:to="lab_lgn_ContractWithCustomerAssetAfterAllowanceForCreditLossRetentions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019eb2fa-0349-7544-a659-d2665ca1ef0f_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_019eb2fa-0349-79da-892c-c97b974c7122_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities, net</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Income Tax Liabilities, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DeferredIncomeTaxLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:to="lab_us-gaap_DeferredIncomeTaxLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_019eb2fa-0349-7cad-95b5-19e754db0139_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019eb2fa-026d-7f97-b73b-4c3bb511e077_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss attributable to Legence</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrTerminationDate" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrTerminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrTerminationDate" xlink:to="lab_ecd_TrdArrTerminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestTable_019eb2fa-0349-71a9-aa2d-b4f1717e9a00_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Table]</link:label>
    <link:label id="lab_us-gaap_MinorityInterestTable_label_en-US" xlink:label="lab_us-gaap_MinorityInterestTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestTable" xlink:to="lab_us-gaap_MinorityInterestTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_019eb2fa-026d-784d-ad49-9dba22790f3f_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted-average Remaining Life (in years)</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Acquired, Weighted-Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableTrade_019eb2fa-03d6-7dbc-8003-06f7f44ba868_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableTrade_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accounts Payable, Trade</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncreaseDecreaseInAccountsPayableTrade"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableTrade" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_019eb2fa-026d-7540-a183-b10f2ac39af8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_019eb2fa-0349-72d0-8905-ab2f2dee4a88_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Finite-Lived</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibles" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Total Shareholder Return [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsTotalShareholderRtnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_label_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MnpiDiscTimedForCompValFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MnpiDiscTimedForCompValFlag" xlink:to="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_019eb2fa-0349-7c69-b6cb-2b634dd93e49_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative assets</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Subject to Master Netting Arrangement, after Offset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:to="lab_us-gaap_DerivativeAssetAfterOffsetSubjectToMasterNettingArrangement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_019eb2fa-026d-74a5-aafe-041df60d70ac_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAssetsNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssetsNoncurrent" xlink:to="lab_us-gaap_OtherAssetsNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_019eb2fa-026d-7e2a-a65f-707f62ee8449_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_019eb2fa-03d6-704b-a2ec-e7c6875a9198_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Consideration paid for acquisitions, net of cash acquired</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Net of Cash Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesNetOfCashAcquired" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeAssetsCurrent_019eb2fa-026d-76e8-b7fb-ae8cd87cf0b7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swaps</link:label>
    <link:label id="lab_us-gaap_DerivativeAssetsCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeAssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Asset, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeAssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeAssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeAssetsCurrent" xlink:to="lab_us-gaap_DerivativeAssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_019eb2fa-03d6-7c8d-a6a6-ad55f7933955_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_019eb2fa-03d6-7b40-8aa8-7e81b218f6ec_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss on debt extinguishment</link:label>
    <link:label id="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt_label_en-US" xlink:label="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Extinguishment of Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GainsLossesOnExtinguishmentOfDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:to="lab_us-gaap_GainsLossesOnExtinguishmentOfDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019eb2fa-0349-7762-8a8f-eafa3eab8b75_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued and other current liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_019eb2fa-0349-75c5-aca8-39386fc50b35_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Accrued and other current liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019eb2fa-0349-74ed-b50f-3096c2946abe_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_019eb2fa-0349-71f9-876c-4545f3b493bc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic, by Common Class, Including Two-Class Method [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:to="lab_us-gaap_ScheduleOfEarningsPerShareBasicByCommonClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_019eb2fa-026d-75b1-be51-540cb4aad34e_verboseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGoodwillTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGoodwillTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGoodwillTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfGoodwillTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGoodwillTable" xlink:to="lab_us-gaap_ScheduleOfGoodwillTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019eb2fa-0349-7113-b5b8-1349e39e2ddd_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_019eb2fa-026d-7251-b461-6982ec401ec7_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Financial Information</link:label>
    <link:label id="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Financial Information Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalFinancialInformationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:to="lab_us-gaap_AdditionalFinancialInformationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019eb2fa-0349-7bc2-85c6-17bad23cc493_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019eb2fa-03d6-7ed6-a508-f8a5106de5cd_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_NumberOfProfessionalCorporationsContracted_019eb2fa-0349-7d73-9fb3-fb34ddf1b73b_terseLabel_en-US" xlink:label="lab_lgn_NumberOfProfessionalCorporationsContracted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of professional corporations contracted</link:label>
    <link:label id="lab_lgn_NumberOfProfessionalCorporationsContracted_label_en-US" xlink:label="lab_lgn_NumberOfProfessionalCorporationsContracted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Professional Corporations Contracted</link:label>
    <link:label id="lab_lgn_NumberOfProfessionalCorporationsContracted_documentation_en-US" xlink:label="lab_lgn_NumberOfProfessionalCorporationsContracted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Professional Corporations Contracted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_NumberOfProfessionalCorporationsContracted" xlink:href="lgn-20260630.xsd#lgn_NumberOfProfessionalCorporationsContracted"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_019eb2fa-0349-782b-9979-6703c931a79f_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">(Loss) income before income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent_019eb2fa-03d6-710a-aa7c-d8fccd5ba3c9_terseLabel_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effects of exercise of underwriters' overallotment option</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent_label_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Percent</link:label>
    <link:label id="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent_documentation_en-US" xlink:label="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:href="lgn-20260630.xsd#lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:to="lab_lgn_StockIssuedDuringPeriodSharesConversionOfConvertibleSecuritiesPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019eb2fa-0349-7209-ae23-278d0cd6a97b_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and contingencies (Note 18)</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed_019eb2fa-026d-7da4-9a42-42bee75c755c_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash tax savings (as percent)</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Cash Tax Savings Owed</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Cash Tax Savings Owed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementCashTaxSavingsOwed"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:to="lab_lgn_TaxReceivableAgreementCashTaxSavingsOwed" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_019eb2fa-026d-7fa9-807a-3483ea14c264_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Carrying Amount</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsGross_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, before Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_019eb2fa-0349-7d3d-99c5-8404f73688d5_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:to="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019eb2fa-026d-718e-82ad-127eeb384d62_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019eb2fa-03d6-79f0-a79d-be4243600f72_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equity in earnings of joint venture</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019eb2fa-03d6-769a-a2e5-288833311392_negatedNetLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedNetLabel" xlink:type="resource" xml:lang="en-US">Equity in earnings of joint venture</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_EngineeringConsultingMember_019eb2fa-026d-7df3-877f-545842986c3a_terseLabel_en-US" xlink:label="lab_lgn_EngineeringConsultingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Engineering &amp; Consulting</link:label>
    <link:label id="lab_lgn_EngineeringConsultingMember_label_en-US" xlink:label="lab_lgn_EngineeringConsultingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Engineering &amp; Consulting [Member]</link:label>
    <link:label id="lab_lgn_EngineeringConsultingMember_documentation_en-US" xlink:label="lab_lgn_EngineeringConsultingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Engineering &amp; Consulting</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_EngineeringConsultingMember" xlink:href="lgn-20260630.xsd#lgn_EngineeringConsultingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_EngineeringConsultingMember" xlink:to="lab_lgn_EngineeringConsultingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxContingencyTable_019eb2fa-03d6-71cc-8108-f85e80c2c7ce_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxContingencyTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxContingencyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Contingency [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxContingencyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxContingencyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxContingencyTable" xlink:to="lab_us-gaap_IncomeTaxContingencyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid_019eb2fa-026d-7acd-927d-fc8e4a550952_terseLabel_en-US" xlink:label="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Decrease) increase in Property and equipment additions included in Accounts payable</link:label>
    <link:label id="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid_label_en-US" xlink:label="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:label id="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid_documentation_en-US" xlink:label="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) In Capital Expenditures Incurred but Not yet Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:href="lgn-20260630.xsd#lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:to="lab_lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_019eb2fa-0349-7dac-ada0-bec29188bf90_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillRollForward_019eb2fa-026d-70ce-bb70-a4bf6a36d2f6_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value of Goodwill</link:label>
    <link:label id="lab_us-gaap_GoodwillRollForward_label_en-US" xlink:label="lab_us-gaap_GoodwillRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillRollForward" xlink:to="lab_us-gaap_GoodwillRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_019eb2fa-026d-71af-b712-bb9d9bf0a6e3_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019eb2fa-0349-728c-b035-28a498bf7418_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeNamesMember_019eb2fa-03d6-7cf0-a7be-9b212432c106_terseLabel_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade names</link:label>
    <link:label id="lab_us-gaap_TradeNamesMember_label_en-US" xlink:label="lab_us-gaap_TradeNamesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trade Names [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeNamesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_TradeNamesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeNamesMember" xlink:to="lab_us-gaap_TradeNamesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_019eb2fa-03d6-71d5-a664-6ec34ec3bfed_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_019eb2fa-026d-7e3b-ac47-476882f25d4e_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventories</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019eb2fa-0349-7d8a-bd4d-ad7344924715_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019eb2fa-0349-769e-be64-ff63675c1836_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019eb2fa-0349-7975-af20-bce91c004c6f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 3</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019eb2fa-026d-7b2d-8991-584280b0e8ba_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_SuretyBondsOutstanding_019eb2fa-0349-75d5-b312-ee6acb3e6182_terseLabel_en-US" xlink:label="lab_lgn_SuretyBondsOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding surety bonds</link:label>
    <link:label id="lab_lgn_SuretyBondsOutstanding_label_en-US" xlink:label="lab_lgn_SuretyBondsOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Surety Bonds, Outstanding</link:label>
    <link:label id="lab_lgn_SuretyBondsOutstanding_documentation_en-US" xlink:label="lab_lgn_SuretyBondsOutstanding" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Surety Bonds, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_SuretyBondsOutstanding" xlink:href="lgn-20260630.xsd#lgn_SuretyBondsOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_SuretyBondsOutstanding" xlink:to="lab_lgn_SuretyBondsOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019eb2fa-0349-7988-bd4d-0f87183228b4_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019eb2fa-03d6-7e5c-bdda-e9315506eac3_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Owners ownership of Legence Holdings Common Units (as percent)</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_019eb2fa-026d-72dc-8c26-11e4c32218ec_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiability_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiability" xlink:to="lab_us-gaap_ContractWithCustomerLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_019eb2fa-03d6-7961-af4a-706c8e8f3eec_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:to="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_019eb2fa-0349-715f-bbcb-60ddd078da06_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Term loan payments</link:label>
    <link:label id="lab_us-gaap_RepaymentsOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Repayments of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RepaymentsOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RepaymentsOfSecuredDebt" xlink:to="lab_us-gaap_RepaymentsOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease_019eb2fa-0349-7cb9-a1f5-cc4e1b90b533_terseLabel_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in tax receivable agreement liability</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease_label_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Liability, Increase (Decrease)</link:label>
    <link:label id="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease_documentation_en-US" xlink:label="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Tax Receivable Agreement, Liability, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:href="lgn-20260630.xsd#lgn_TaxReceivableAgreementLiabilityIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:to="lab_lgn_TaxReceivableAgreementLiabilityIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019eb2fa-03d6-7c79-8524-01bbb8c4ee20_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable_019eb2fa-03d6-79cc-bb30-5198e558ae9d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Table]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresTable"/>
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    <link:label id="lab_dei_LegalEntityAxis_019eb2fa-026d-7522-ab03-9d077cc985cb_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract_019eb2fa-0349-73f9-b592-4171fc73d68c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets acquired based on fair values:</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less), and Goodwill [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredGoodwillAndLiabilitiesAssumedNetAbstract"/>
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    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee_019eb2fa-0349-7757-b81d-798f903e6043_terseLabel_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum purchase shares during offering period</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee_label_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Shares During Offering Period, Per Employee</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee_documentation_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Shares During Offering Period, Per Employee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee" xlink:href="lgn-20260630.xsd#lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee"/>
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    <link:label id="lab_us-gaap_SelfInsuranceReserveCurrent_019eb2fa-03d6-76b8-be8d-c211bb23a4cc_terseLabel_en-US" xlink:label="lab_us-gaap_SelfInsuranceReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Self Insurance Reserve, Current</link:label>
    <link:label id="lab_us-gaap_SelfInsuranceReserveCurrent_label_en-US" xlink:label="lab_us-gaap_SelfInsuranceReserveCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Self Insurance Reserve, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SelfInsuranceReserveCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SelfInsuranceReserveCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SelfInsuranceReserveCurrent" xlink:to="lab_us-gaap_SelfInsuranceReserveCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_019eb2fa-026d-7d97-8b65-7671abce4d1a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other accrued liabilities</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_019eb2fa-0349-7337-b92d-fa25d84bd524_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BaseRateMember_019eb2fa-0349-76c4-babe-a55d6971e4b7_terseLabel_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Base Rate</link:label>
    <link:label id="lab_us-gaap_BaseRateMember_label_en-US" xlink:label="lab_us-gaap_BaseRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Base Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BaseRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BaseRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BaseRateMember" xlink:to="lab_us-gaap_BaseRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember_019eb2fa-0349-78d2-a897-ac2d7dde305a_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Noncontrolling Interest</link:label>
    <link:label id="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Gain (Loss), Net, Cash Flow Hedge, Noncontrolling Interest [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember" xlink:to="lab_us-gaap_AccumulatedGainLossNetCashFlowHedgeNoncontrollingInterestMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompNotYetDeterminedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:to="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonNeosMember_terseLabel_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-NEOs</link:label>
    <link:label id="lab_ecd_NonNeosMember_label_en-US" xlink:label="lab_ecd_NonNeosMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-NEOs [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonNeosMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonNeosMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonNeosMember" xlink:to="lab_ecd_NonNeosMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019eb2fa-03d6-78cf-aafe-1efeaa769f86_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Nature of Operations and Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_019eb2fa-0349-7391-81f4-144b615984cb_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ComprehensiveIncomeNetOfTaxIncludingPortionAttributableToNoncontrollingInterest"/>
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    <link:label id="lab_lgn_RightOfUseAssetModificationsForOperatingLeases_019eb2fa-026d-7969-940c-7e825f1827a2_terseLabel_en-US" xlink:label="lab_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use asset modifications for operating leases</link:label>
    <link:label id="lab_lgn_RightOfUseAssetModificationsForOperatingLeases_label_en-US" xlink:label="lab_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset Modifications For Operating Leases</link:label>
    <link:label id="lab_lgn_RightOfUseAssetModificationsForOperatingLeases_documentation_en-US" xlink:label="lab_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Right-Of-Use Asset Modifications For Operating Leases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:href="lgn-20260630.xsd#lgn_RightOfUseAssetModificationsForOperatingLeases"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:to="lab_lgn_RightOfUseAssetModificationsForOperatingLeases" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019eb2fa-03d6-7537-ad63-1b13dae073c2_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019eb2fa-03d6-7f2d-955e-09223ac356a7_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019eb2fa-0349-76c1-ad12-b30ed047321b_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019eb2fa-03d6-7701-8557-fed8a5ffc150_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_019eb2fa-0349-7e45-ad76-9ffc589cc40b_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase price of common stock, percent</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_019eb2fa-026d-7e85-849c-34b72393750f_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Debt Obligations</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Debt [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDebtTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_019eb2fa-0349-7055-b442-3abbfb02b8ab_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange of Class B Common Stock to Class A Common Stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_019eb2fa-0349-7a80-8cfb-6c3afdba77fe_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Effects of exercise of underwriters' overallotment option (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_019eb2fa-0349-75ea-be2d-878f0c172cdc_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_019eb2fa-0349-7126-923f-ac1505ca84c0_terseLabel_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:label id="lab_srt_NameOfMajorCustomerDomain_label_en-US" xlink:label="lab_srt_NameOfMajorCustomerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_NameOfMajorCustomerDomain" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_NameOfMajorCustomerDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_NameOfMajorCustomerDomain" xlink:to="lab_srt_NameOfMajorCustomerDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019eb2fa-026d-7da7-9fa5-a03d64f3d777_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_019eb2fa-0349-71f0-ab5e-a4af22d448a7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Assets and Derivative Liabilities</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Derivative Instruments in Statement of Financial Position, Fair Value [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:to="lab_us-gaap_ScheduleOfDerivativeInstrumentsInStatementOfFinancialPositionFairValueTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019eb2fa-03d6-726e-ac99-04fa34232eba_verboseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_019eb2fa-03d6-76dd-97ee-64d4c0bbb82f_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss per share&#8212;basic (in usd per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ContractsReceivableRetentions_019eb2fa-0349-79fb-8cff-c9797f6d12ef_terseLabel_en-US" xlink:label="lab_lgn_ContractsReceivableRetentions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contracts receivable, retentions</link:label>
    <link:label id="lab_lgn_ContractsReceivableRetentions_label_en-US" xlink:label="lab_lgn_ContractsReceivableRetentions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contracts Receivable, Retentions</link:label>
    <link:label id="lab_lgn_ContractsReceivableRetentions_documentation_en-US" xlink:label="lab_lgn_ContractsReceivableRetentions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contracts Receivable, Retentions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ContractsReceivableRetentions" xlink:href="lgn-20260630.xsd#lgn_ContractsReceivableRetentions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ContractsReceivableRetentions" xlink:to="lab_lgn_ContractsReceivableRetentions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_019eb2fa-03d6-7cd1-aa4a-0ac1d34754e4_terseLabel_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_us-gaap_ContractWithCustomerLiabilityCurrent_label_en-US" xlink:label="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contract with Customer, Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ContractWithCustomerLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:to="lab_us-gaap_ContractWithCustomerLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_019eb2fa-0349-7a4a-b9cc-1813ebe64f62_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019eb2fa-0349-7728-9376-e380734c8306_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration_019eb2fa-0349-7d01-818a-23373d35ae02_terseLabel_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contract liabilities</link:label>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration_label_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Deferred Consideration</link:label>
    <link:label id="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration_documentation_en-US" xlink:label="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Deferred Consideration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:href="lgn-20260630.xsd#lgn_BusinessCombinationConsiderationTransferredDeferredConsideration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:to="lab_lgn_BusinessCombinationConsiderationTransferredDeferredConsideration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019eb2fa-0349-7fcb-ada4-746286569a23_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits_019fe95e-ed65-7804-ae81-5c2a7ae986c3_verboseLabel_en-US" xlink:label="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Effect of exchange of LGN B Units related to exercise of underwriters' overallotment option and Subsequent Secondary Offering (in shares)</link:label>
    <link:label id="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits_label_en-US" xlink:label="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable To Dilutive Effect Of Conversion Of Stock Units</link:label>
    <link:label id="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits_documentation_en-US" xlink:label="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Incremental Common Shares Attributable To Dilutive Effect Of Conversion Of Stock Units</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:href="lgn-20260630.xsd#lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:to="lab_lgn_IncrementalCommonSharesAttributableToDilutiveEffectOfConversionOfStockUnits" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_019eb2fa-03d6-7649-b2ad-4e3ecf28578e_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_OneCustomerMember_019eb2fa-026d-7873-97bb-653b4eba16f0_terseLabel_en-US" xlink:label="lab_lgn_OneCustomerMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">One Customer</link:label>
    <link:label id="lab_lgn_OneCustomerMember_label_en-US" xlink:label="lab_lgn_OneCustomerMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">One Customer [Member]</link:label>
    <link:label id="lab_lgn_OneCustomerMember_documentation_en-US" xlink:label="lab_lgn_OneCustomerMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">One Customer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_OneCustomerMember" xlink:href="lgn-20260630.xsd#lgn_OneCustomerMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_OneCustomerMember" xlink:to="lab_lgn_OneCustomerMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019eb2fa-03d6-7194-924a-1540ac97b079_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019eb2fa-0349-70e7-b58e-85f909137169_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2026/elts/srt-2026.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DeferredConsiderationCurrent_019ed07d-fc1d-708d-8a1c-43c2dccbd699_verboseLabel_en-US" xlink:label="lab_lgn_DeferredConsiderationCurrent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Deferred consideration</link:label>
    <link:label id="lab_lgn_DeferredConsiderationCurrent_label_en-US" xlink:label="lab_lgn_DeferredConsiderationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Consideration, Current</link:label>
    <link:label id="lab_lgn_DeferredConsiderationCurrent_documentation_en-US" xlink:label="lab_lgn_DeferredConsiderationCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Consideration, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DeferredConsiderationCurrent" xlink:href="lgn-20260630.xsd#lgn_DeferredConsiderationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DeferredConsiderationCurrent" xlink:to="lab_lgn_DeferredConsiderationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage_019eb2fa-03d6-7cef-900b-e16abc964a62_terseLabel_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award type, percentage</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage_label_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Award, Percentage</link:label>
    <link:label id="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage_documentation_en-US" xlink:label="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Award, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:href="lgn-20260630.xsd#lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:to="lab_lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_019eb2fa-0349-7828-aaf6-fdd5ff45a010_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term loan borrowings (including $15,000 and $2,495 in 2026 and 2025, respectively, from related parties)</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Secured Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromIssuanceOfSecuredDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfSecuredDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019eb2fa-026d-70e4-8d3a-c25e5ff397d4_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_019eb2fa-0349-7c64-be19-51d0ac097457_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosureItemAmountsDomain_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueDisclosureItemAmountsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:to="lab_us-gaap_FairValueDisclosureItemAmountsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_019eb2fa-0349-780a-a5e4-09e9a169df39_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Current portion of long-term debt</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Liability Assumed, Long-Term Debt, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentLiabilitiesLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_NoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NoncontrollingInterestAbstract" xlink:to="lab_us-gaap_NoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_Total2026AcquisitionsMember_019eb2fa-0349-7632-9c5c-28af3cb486d3_terseLabel_en-US" xlink:label="lab_lgn_Total2026AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total 2026 Acquisitions</link:label>
    <link:label id="lab_lgn_Total2026AcquisitionsMember_label_en-US" xlink:label="lab_lgn_Total2026AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total 2026 Acquisitions [Member]</link:label>
    <link:label id="lab_lgn_Total2026AcquisitionsMember_documentation_en-US" xlink:label="lab_lgn_Total2026AcquisitionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Total 2026 Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_Total2026AcquisitionsMember" xlink:href="lgn-20260630.xsd#lgn_Total2026AcquisitionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_Total2026AcquisitionsMember" xlink:to="lab_lgn_Total2026AcquisitionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_019eb2fa-026d-7184-84e7-b743db91fa69_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019eb2fa-0349-7dc6-982c-6ad6bcfa2ae1_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk, percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019eb2fa-03d6-72ae-9771-d3e0fb5ad8e2_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_019eb2fa-0349-72f7-b326-bcc39ecb0c37_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingRelationshipDomain_label_en-US" xlink:label="lab_us-gaap_HedgingRelationshipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Relationship [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingRelationshipDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingRelationshipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingRelationshipDomain" xlink:to="lab_us-gaap_HedgingRelationshipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019eb2fa-03d6-7102-beef-7342bfd2037b_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and stockholders' equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquisitionRelatedCostsMember_019eb2fa-03d6-70f3-b08e-dc90ee09fc25_terseLabel_en-US" xlink:label="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment, Acquisition-Related Cost</link:label>
    <link:label id="lab_us-gaap_AcquisitionRelatedCostsMember_label_en-US" xlink:label="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Nonrecurring Adjustment, Acquisition-Related Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquisitionRelatedCostsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AcquisitionRelatedCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquisitionRelatedCostsMember" xlink:to="lab_us-gaap_AcquisitionRelatedCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests_019eb2fa-0349-7558-b166-10420fa64c34_terseLabel_en-US" xlink:label="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contribution from Legence Parent for Series A Interests and Restricted Series C Interests</link:label>
    <link:label id="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests_label_en-US" xlink:label="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contributions From Parent I For Series A Interests And Restricted Series C Interests</link:label>
    <link:label id="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests_documentation_en-US" xlink:label="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Contributions From Parent I For Series A Interests And Restricted Series C Interests</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:href="lgn-20260630.xsd#lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:to="lab_lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019eb2fa-03d6-7b18-bd31-a5c3bfbd5656_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterest_019eb2fa-026d-75f8-9cdc-c1de6c900c1f_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Noncontrolling interests</link:label>
    <link:label id="lab_us-gaap_MinorityInterest_label_en-US" xlink:label="lab_us-gaap_MinorityInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_MinorityInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterest" xlink:to="lab_us-gaap_MinorityInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_019eb2fa-0349-77ec-b1d9-731833c6659e_terseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable</link:label>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_019eb2fa-0349-7cb8-8427-1f2ed5d0bf1e_verboseLabel_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Promissory notes</link:label>
    <link:label id="lab_us-gaap_NotesPayableOtherPayablesMember_label_en-US" xlink:label="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Other Payables [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NotesPayableOtherPayablesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NotesPayableOtherPayablesMember" xlink:to="lab_us-gaap_NotesPayableOtherPayablesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019eb2fa-03d6-7266-9df8-becb088d4921_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019eb2fa-03d6-72ca-aecf-752f9c211732_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_019eb2fa-0349-79ec-b2e8-b5d1da6895ec_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Accounts Receivable Net</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019eb2fa-03d6-78b9-bb12-d08877241869_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019eb2fa-0349-716a-ad16-806cac791a85_negatedLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_019eb2fa-0349-7a83-8bf1-05337019726c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other income, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ParentMember_019eb2fa-03d6-7c23-8bd0-e319038a717b_terseLabel_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Legence Stockholders' Equity</link:label>
    <link:label id="lab_us-gaap_ParentMember_label_en-US" xlink:label="lab_us-gaap_ParentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ParentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ParentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ParentMember" xlink:to="lab_us-gaap_ParentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019eb2fa-03d6-782f-b420-54572037162b_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_019eb2fa-026d-7e07-9817-8c9e791625f3_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026 (six months remaining)</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Finite-Lived, Estimated Amortization Expense, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceClaimsMember_019eb2fa-03d6-7b4f-9b4c-5b34bb54834f_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceClaimsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance Claims</link:label>
    <link:label id="lab_us-gaap_InsuranceClaimsMember_label_en-US" xlink:label="lab_us-gaap_InsuranceClaimsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Claims [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceClaimsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InsuranceClaimsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceClaimsMember" xlink:to="lab_us-gaap_InsuranceClaimsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:to="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_019eb2fa-026d-78ea-8fdb-04ab200534c5_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock, price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_label_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SaleOfStockPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_019eb2fa-0349-7306-99d3-92718027089c_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange of Class B Common Stock to Class A Common Stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities"/>
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    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_019eb2fa-026d-7dac-9503-47933f600aa9_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivablesNetCurrent_019eb2fa-03d6-724c-a700-cb37d084370a_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_ReceivablesNetCurrent_019eb2fa-03d6-703b-a395-bb3d9217ebb9_totalLabel_en-US" xlink:label="lab_us-gaap_ReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Accounts receivable, net</link:label>
    <link:label id="lab_us-gaap_ReceivablesNetCurrent_label_en-US" xlink:label="lab_us-gaap_ReceivablesNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivables, Net, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivablesNetCurrent" xlink:to="lab_us-gaap_ReceivablesNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_019eb2fa-026d-7601-a34e-c5e399b07479_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, $0.01 par value, 50,000,000 shares authorized, no shares issued or outstanding as of June&#160;30, 2026 and December&#160;31, 2025</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_PreferredStockValue"/>
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    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AdjToCompAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAxis" xlink:to="lab_ecd_AdjToCompAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_019eb2fa-0349-7b15-ba74-929fe0b49802_negatedLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Gain reclassified from AOCI to Interest expense</link:label>
    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax_label_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification from Accumulated Other Comprehensive Income, Current Period, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:to="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_019eb2fa-03d6-7832-9841-311591ef5aef_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationDomain_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationDomain" xlink:to="lab_us-gaap_HedgingDesignationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockDomain_019eb2fa-0349-7606-b0ac-f6380c747757_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ClassOfStockDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockDomain" xlink:to="lab_us-gaap_ClassOfStockDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPaidNet_019eb2fa-0349-7a06-abf2-a1d3a4c4774d_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest paid, net of interest rate swaps</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_019eb2fa-03d6-7c89-ad82-0122950340d4_terseLabel_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:label id="lab_us-gaap_HedgingDesignationAxis_label_en-US" xlink:label="lab_us-gaap_HedgingDesignationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Hedging Designation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_HedgingDesignationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_HedgingDesignationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_HedgingDesignationAxis" xlink:to="lab_us-gaap_HedgingDesignationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock_019eb2fa-026d-7544-b149-a455ad67b78f_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Ownership of Legence Holdings</link:label>
    <link:label id="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Less than Wholly Owned Subsidiary, Parent Ownership Interest, Effects of Changes, Net [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock" xlink:to="lab_us-gaap_ConsolidationLessThanWhollyOwnedSubsidiaryParentOwnershipInterestEffectsOfChangesNetTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CreditFacilityAxis_019eb2fa-0349-7ec2-9b41-1be0c296067a_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityAxis_label_en-US" xlink:label="lab_us-gaap_CreditFacilityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CreditFacilityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityAxis" xlink:to="lab_us-gaap_CreditFacilityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_terseLabel_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Available</link:label>
    <link:label id="lab_ecd_TrdArrSecuritiesAggAvailAmt_label_en-US" xlink:label="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Securities Aggregate Available Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrSecuritiesAggAvailAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrSecuritiesAggAvailAmt" xlink:to="lab_ecd_TrdArrSecuritiesAggAvailAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_SelfInsuranceThresholdForStopLossInsurance_019eb2fa-03d6-7633-bf57-4ed8a56a9052_terseLabel_en-US" xlink:label="lab_lgn_SelfInsuranceThresholdForStopLossInsurance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Self insurance coverage</link:label>
    <link:label id="lab_lgn_SelfInsuranceThresholdForStopLossInsurance_label_en-US" xlink:label="lab_lgn_SelfInsuranceThresholdForStopLossInsurance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Self Insurance, Threshold For Stop-Loss Insurance</link:label>
    <link:label id="lab_lgn_SelfInsuranceThresholdForStopLossInsurance_documentation_en-US" xlink:label="lab_lgn_SelfInsuranceThresholdForStopLossInsurance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Self Insurance, Threshold For Stop-Loss Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_SelfInsuranceThresholdForStopLossInsurance" xlink:href="lgn-20260630.xsd#lgn_SelfInsuranceThresholdForStopLossInsurance"/>
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    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_019eb2fa-03d6-7cbd-a010-82e8d5f0bb22_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net of current portion (including $97,162 and $84,735 as of June&#160;30, 2026 and December&#160;31, 2025, respectively, from related parties)</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_019eb2fa-03d6-7079-ae2a-84fdbfc62bde_verboseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Long-term debt, net of current portion</link:label>
    <link:label id="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations_label_en-US" xlink:label="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt and Lease Obligation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermDebtAndCapitalLeaseObligations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:to="lab_us-gaap_LongTermDebtAndCapitalLeaseObligations" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_019eb2fa-0349-78c5-8c6e-f11367914597_terseLabel_en-US" xlink:label="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_label_en-US" xlink:label="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite Lived Intangible Assets Amortization Expense After Year Four</link:label>
    <link:label id="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour_documentation_en-US" xlink:label="lab_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite Lived Intangible Assets Amortization Expense After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" xlink:href="lgn-20260630.xsd#lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour"/>
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    <link:label id="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities_019eb2fa-026d-77e4-83ac-76e70c3d6311_negatedTerseLabel_en-US" xlink:label="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reclassification of vested Legence Parent Series A Interests from liabilities</link:label>
    <link:label id="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities_label_en-US" xlink:label="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments To Member's Equity, Reclassification Of Vested Parent Interests From Liabilities</link:label>
    <link:label id="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities_documentation_en-US" xlink:label="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments To Member's Equity, Reclassification Of Vested Parent Interests From Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:href="lgn-20260630.xsd#lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:to="lab_lgn_AdjustmentsToMembersEquityReclassificationOfVestedParentInterestsFromLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_UnderwritersOptionPeriod_019eb2fa-0349-7103-b82e-4c82d4686d3a_terseLabel_en-US" xlink:label="lab_lgn_UnderwritersOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underwriters option period</link:label>
    <link:label id="lab_lgn_UnderwritersOptionPeriod_label_en-US" xlink:label="lab_lgn_UnderwritersOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underwriters Option Period</link:label>
    <link:label id="lab_lgn_UnderwritersOptionPeriod_documentation_en-US" xlink:label="lab_lgn_UnderwritersOptionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Underwriters Option Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_UnderwritersOptionPeriod" xlink:href="lgn-20260630.xsd#lgn_UnderwritersOptionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_UnderwritersOptionPeriod" xlink:to="lab_lgn_UnderwritersOptionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_019eb2fa-0349-7933-b3c0-54e3cb8406ae_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_019eb2fa-026d-7a6f-8244-27c29716dae1_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounts payable</link:label>
    <link:label id="lab_us-gaap_AccountsPayableCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounts Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AccountsPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableCurrent" xlink:to="lab_us-gaap_AccountsPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019eb2fa-0349-74f1-a289-e89958c1aaf3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_019eb2fa-026d-7d1e-8283-9164bbc5ee32_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other</link:label>
    <link:label id="lab_us-gaap_OtherNoncashIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNoncashIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Noncash Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNoncashIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_OtherNoncashIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNoncashIncomeExpense" xlink:to="lab_us-gaap_OtherNoncashIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019eb2fa-0349-736c-9a03-36c667660063_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019eb2fa-026d-70d2-952a-34bde0286620_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total consideration transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019eb2fa-026d-733b-8469-ed5fdb049b38_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total consideration transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount_019eb2fa-0349-764f-b26a-e997f4859d46_terseLabel_en-US" xlink:label="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit agreement amendment fees</link:label>
    <link:label id="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount_label_en-US" xlink:label="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Amendment Fee, Amount</link:label>
    <link:label id="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount_documentation_en-US" xlink:label="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Line Of Credit Facility, Amendment Fee, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:href="lgn-20260630.xsd#lgn_LineOfCreditFacilityAmendmentFeeAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:to="lab_lgn_LineOfCreditFacilityAmendmentFeeAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019eb2fa-026d-77b6-b926-266272d60b9a_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019eb2fa-0349-7ca6-b078-9c68ac0e010f_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_ProgramAndProjectManagementMember_019eb2fa-0349-7022-b33d-26af2cf2f6d6_terseLabel_en-US" xlink:label="lab_lgn_ProgramAndProjectManagementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Program &amp; Project Management</link:label>
    <link:label id="lab_lgn_ProgramAndProjectManagementMember_label_en-US" xlink:label="lab_lgn_ProgramAndProjectManagementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Program And Project Management [Member]</link:label>
    <link:label id="lab_lgn_ProgramAndProjectManagementMember_documentation_en-US" xlink:label="lab_lgn_ProgramAndProjectManagementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Program And Project Management</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_ProgramAndProjectManagementMember" xlink:href="lgn-20260630.xsd#lgn_ProgramAndProjectManagementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_ProgramAndProjectManagementMember" xlink:to="lab_lgn_ProgramAndProjectManagementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019fc6e1-9b95-7178-9dae-0f99117c8c7f_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Goodwill impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_019fda03-748c-7458-a547-a5ebdbb631d6_negatedLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Impairment</link:label>
    <link:label id="lab_us-gaap_GoodwillImpairmentLoss_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill, Impairment Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GoodwillImpairmentLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillImpairmentLoss" xlink:to="lab_us-gaap_GoodwillImpairmentLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI_019eb2fa-0349-781c-95da-4b673fd6dee3_terseLabel_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contribution from Legence Parent for Series A Interests and Restricted Series C Interests</link:label>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI_label_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid In Capital, Contributions From Parent I</link:label>
    <link:label id="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI_documentation_en-US" xlink:label="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Adjustments To Additional Paid In Capital, Contributions From Parent I</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:href="lgn-20260630.xsd#lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:to="lab_lgn_AdjustmentsToAdditionalPaidInCapitalContributionsFromParentI" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019eb2fa-03d6-7dab-97ba-150339fa7ba8_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_IMDMember_019eb2fa-0349-79e0-b72b-0aa96b33657b_terseLabel_en-US" xlink:label="lab_lgn_IMDMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">IMD</link:label>
    <link:label id="lab_lgn_IMDMember_label_en-US" xlink:label="lab_lgn_IMDMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">IMD [Member]</link:label>
    <link:label id="lab_lgn_IMDMember_documentation_en-US" xlink:label="lab_lgn_IMDMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">IMD</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_IMDMember" xlink:href="lgn-20260630.xsd#lgn_IMDMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_IMDMember" xlink:to="lab_lgn_IMDMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019eb2fa-0349-73d7-bf28-1930d52ad6bb_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments and Joint Ventures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:to="lab_us-gaap_EquityMethodInvestmentsAndJointVenturesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_019eb2fa-0349-7732-8ac4-6ece43d1deaa_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR)</link:label>
    <link:label id="lab_us-gaap_SecuredOvernightFinancingRateSofrMember_label_en-US" xlink:label="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Overnight Financing Rate (SOFR) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_SecuredOvernightFinancingRateSofrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:to="lab_us-gaap_SecuredOvernightFinancingRateSofrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_019fd845-c1bb-7fba-9d91-12cc4d01056f_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of Class A Common Stock under stock-based compensation plans (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Issued, Shares, Share-Based Payment Arrangement, after Forfeiture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProfitLoss_019eb2fa-026d-7d6b-81f0-8cf9fec67595_totalLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019eb2fa-026d-7949-ada1-9fd9addff8f3_terseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019eb2fa-026d-780e-bda0-37d8a022a812_netLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net (loss) income</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_019eb2fa-026d-718e-9788-9daf14db3bed_verboseLabel_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_ProfitLoss_label_en-US" xlink:label="lab_us-gaap_ProfitLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProfitLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProfitLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProfitLoss" xlink:to="lab_us-gaap_ProfitLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_019eb2fa-03d6-7563-ab27-9f390dfbfa9c_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets obtained in exchange for new finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Finance Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForFinanceLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_019eb2fa-026e-7e95-b06a-e45844f0ff5b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_019eb2fa-03d6-7c3e-84fe-e6f6d6c6ea51_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest rate swap instruments</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_019eb2fa-03d6-73dd-8625-7e273dee99aa_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:to="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_NonPeoNeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoMember" xlink:to="lab_ecd_NonPeoNeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019eb2fa-026d-797c-b912-f7a4c967ebe4_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2026/dei-2026.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_019eb2fa-0349-7587-9b92-ad1f6e845319_terseLabel_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Right-of-use assets obtained in exchange for new operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Right-of-Use Asset Obtained in Exchange for Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:to="lab_us-gaap_RightOfUseAssetObtainedInExchangeForOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DepreciationNonproduction_019eb2fa-03d6-7045-918f-74919e3db81d_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationNonproduction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciation of property and equipment</link:label>
    <link:label id="lab_us-gaap_DepreciationNonproduction_label_en-US" xlink:label="lab_us-gaap_DepreciationNonproduction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Nonproduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationNonproduction" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DepreciationNonproduction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationNonproduction" xlink:to="lab_us-gaap_DepreciationNonproduction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ec9b0-9140-72fc-8621-43e042ef51af_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019eb2fa-026d-7397-9fad-8a20378030fb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense (benefit)</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_019eb2fa-026d-7e0f-80f2-ec12b8484110_terseLabel_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk</link:label>
    <link:label id="lab_us-gaap_CustomerConcentrationRiskMember_label_en-US" xlink:label="lab_us-gaap_CustomerConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Customer Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CustomerConcentrationRiskMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CustomerConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CustomerConcentrationRiskMember" xlink:to="lab_us-gaap_CustomerConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_019eb2fa-026d-7b31-a9a4-9596137975fe_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of revenue</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Product and Service Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyNatureDomain_019eb2fa-03d6-7778-8bb0-9099056ede59_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyNatureDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingency, Nature [Domain]</link:label>
    <link:label id="lab_us-gaap_LossContingencyNatureDomain_label_en-US" xlink:label="lab_us-gaap_LossContingencyNatureDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Nature [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyNatureDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyNatureDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyNatureDomain" xlink:to="lab_us-gaap_LossContingencyNatureDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DebtInstrumentVariableRateFloor_019eb2fa-0349-7ecd-b38e-988146e66c8e_terseLabel_en-US" xlink:label="lab_lgn_DebtInstrumentVariableRateFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable rate floor (as percent)</link:label>
    <link:label id="lab_lgn_DebtInstrumentVariableRateFloor_label_en-US" xlink:label="lab_lgn_DebtInstrumentVariableRateFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Variable Rate Floor</link:label>
    <link:label id="lab_lgn_DebtInstrumentVariableRateFloor_documentation_en-US" xlink:label="lab_lgn_DebtInstrumentVariableRateFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Variable Rate Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DebtInstrumentVariableRateFloor" xlink:href="lgn-20260630.xsd#lgn_DebtInstrumentVariableRateFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DebtInstrumentVariableRateFloor" xlink:to="lab_lgn_DebtInstrumentVariableRateFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019eb2fa-026d-7116-a4ea-155bf5c9ad0a_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Increase in cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongTermNotesPayable_019eb2fa-0349-7261-8377-657e760d959b_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermNotesPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Notes payable, noncurrent</link:label>
    <link:label id="lab_us-gaap_LongTermNotesPayable_label_en-US" xlink:label="lab_us-gaap_LongTermNotesPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Payable, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermNotesPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongTermNotesPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermNotesPayable" xlink:to="lab_us-gaap_LongTermNotesPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_IncrementalTermLoanMember_019eb2fa-0349-78d1-9eb7-7a0562b48066_terseLabel_en-US" xlink:label="lab_lgn_IncrementalTermLoanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incremental Term Loan</link:label>
    <link:label id="lab_lgn_IncrementalTermLoanMember_label_en-US" xlink:label="lab_lgn_IncrementalTermLoanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Incremental Term Loan [Member]</link:label>
    <link:label id="lab_lgn_IncrementalTermLoanMember_documentation_en-US" xlink:label="lab_lgn_IncrementalTermLoanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Incremental Term Loan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_IncrementalTermLoanMember" xlink:href="lgn-20260630.xsd#lgn_IncrementalTermLoanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_IncrementalTermLoanMember" xlink:to="lab_lgn_IncrementalTermLoanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities_019eb2fa-0349-76e5-8b22-1438e679ec02_terseLabel_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred offering costs included in Accrued and other current liabilities</link:label>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities_label_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs Included In Accrued And Other Current Liabilities</link:label>
    <link:label id="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities_documentation_en-US" xlink:label="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Offering Costs Included In Accrued And Other Current Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:href="lgn-20260630.xsd#lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:to="lab_lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingencyAccrualCarryingValueCurrent_019eb2fa-0349-785a-8137-bb9a8316f987_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualCarryingValueCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reasonable possible losses in excess of reserves established</link:label>
    <link:label id="lab_us-gaap_LossContingencyAccrualCarryingValueCurrent_label_en-US" xlink:label="lab_us-gaap_LossContingencyAccrualCarryingValueCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Accrual, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyAccrualCarryingValueCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LossContingencyAccrualCarryingValueCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyAccrualCarryingValueCurrent" xlink:to="lab_us-gaap_LossContingencyAccrualCarryingValueCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member_019eb2fa-026d-791d-a63e-fa465ed41e60_terseLabel_en-US" xlink:label="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">3.3750% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:label id="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member_label_en-US" xlink:label="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">3.3750% Interest Rate Swap, Maturing at December 2026 [Member]</link:label>
    <link:label id="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member_documentation_en-US" xlink:label="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">3.3750% Interest Rate Swap, Maturing at December 2026</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:href="lgn-20260630.xsd#lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:to="lab_lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_019eb2fa-03d6-7fcb-b1b6-b08e4f341e9c_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity, Primary Beneficiary [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_VariableInterestEntityPrimaryBeneficiaryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:to="lab_us-gaap_VariableInterestEntityPrimaryBeneficiaryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_019eb2fa-026d-736f-9cae-fcae2d813ca2_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to Legence</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019eb2fa-0349-72e7-8a2f-13531fec42d7_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_019eb2fa-026d-71eb-b021-51361846df78_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of property and equipment</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:to="lab_us-gaap_ProceedsFromSaleOfPropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_019eb2fa-03d6-7c39-9653-9652b8a9637c_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Location, Statement of Financial Position, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementOfFinancialPositionLocationBalanceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:to="lab_us-gaap_StatementOfFinancialPositionLocationBalanceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_019eb2fa-03d6-7f7a-8f42-0781ef338d40_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2026/ecd-2026.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_019eb2fa-0349-78f8-8219-fbdcc8abb27b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_019eb2fa-026d-7583-b6a8-e03d2a94bbc8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosuresLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FederalFundsEffectiveSwapRateMember_019eb2fa-0349-7e0d-8470-95f5c6078806_terseLabel_en-US" xlink:label="lab_us-gaap_FederalFundsEffectiveSwapRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fed Funds Effective Rate Overnight Index Swap Rate</link:label>
    <link:label id="lab_us-gaap_FederalFundsEffectiveSwapRateMember_label_en-US" xlink:label="lab_us-gaap_FederalFundsEffectiveSwapRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fed Funds Effective Rate Overnight Index Swap Rate [Member]</link:label>
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