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  <xs:element id="lgn_ProgramAndProjectManagementMember" abstract="true" name="ProgramAndProjectManagementMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InstallationAndFabricationMember" abstract="true" name="InstallationAndFabricationMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_MaintenanceAndServiceMember" abstract="true" name="MaintenanceAndServiceMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_EngineeringAndConsultingMember" abstract="true" name="EngineeringAndConsultingMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_P2SLPMember" abstract="true" name="P2SLPMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_Other2024AcquisitionMember" abstract="true" name="Other2024AcquisitionMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_AMAConsultingEngineersHoldingsLLCMember" abstract="true" name="AMAConsultingEngineersHoldingsLLCMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A2025AcquisitionsMember" abstract="true" name="A2025AcquisitionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_TheBowersGroupInc.Member" abstract="true" name="TheBowersGroupInc.Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_PaymentsToAcquireBusinessesGrossExpected" abstract="false" name="PaymentsToAcquireBusinessesGrossExpected" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
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  <xs:element id="lgn_BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" abstract="false" name="BusinessCombinationConsiderationTransferredLiabilitiesIncurredHoldback" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_Total2024AcquisitionsMember" abstract="true" name="Total2024AcquisitionsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedAssetAcquiredContractAssets" abstract="false" name="BusinessCombinationRecognizedAssetAcquiredContractAssets" nillable="true" xbrli:periodType="instant" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" abstract="false" name="BusinessCombinationRecognizedAssetAcquiredAssetOperatingLeaseRightOfUseAssets" nillable="true" xbrli:periodType="instant" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" abstract="false" name="BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsAcquiredIncludingGoodwill" nillable="true" xbrli:periodType="instant" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" abstract="false" name="BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedCompensationAndBenefits" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedAndOtherLiabilitiesCurrent" abstract="false" name="BusinessCombinationRecognizedLiabilityAssumedLiabilityAccruedAndOtherLiabilitiesCurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedLiabilityAssumedContractLiability" abstract="false" name="BusinessCombinationRecognizedLiabilityAssumedContractLiability" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" abstract="false" name="BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesCurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesNoncurrent" abstract="false" name="BusinessCombinationRecognizedLiabilityAssumedOperatingLeaseLiabilitiesNoncurrent" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" abstract="false" name="FiniteLivedIntangibleAssetsAmortizationExpenseAfterYearFour" nillable="true" xbrli:periodType="instant" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_ProfessionalCorporationsMember" abstract="true" name="ProfessionalCorporationsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_NumberOfProfessionalCorporationsContracted" abstract="false" name="NumberOfProfessionalCorporationsContracted" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="lgn_DebtInstrumentVariableRateFloor" abstract="false" name="DebtInstrumentVariableRateFloor" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="lgn_DebtInstrumentAdditionalSpreadAdjustmentOnVariableRate" abstract="false" name="DebtInstrumentAdditionalSpreadAdjustmentOnVariableRate" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="lgn_JefferiesFinanceLLCRevolvingLineOfCreditMember" abstract="true" name="JefferiesFinanceLLCRevolvingLineOfCreditMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_OneMonthSOFRMember" abstract="true" name="OneMonthSOFRMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" abstract="false" name="DebtInstrumentCovenantConsolidatedFirstLienNetLeverageRatioMaximum" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="lgn_DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" abstract="false" name="DebtInstrumentThresholdToTestNetLeverageRatioOutstandingBorrowingsComparedToFacilitySizePercentMinimum" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="lgn_PromissoryNotePayableInConnectionWith2022AcquisitionMember" abstract="true" name="PromissoryNotePayableInConnectionWith2022AcquisitionMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_PromissoryNotePayableInConnectionWith2023And2022AcquisitionMember" abstract="true" name="PromissoryNotePayableInConnectionWith2023And2022AcquisitionMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InsuranceRelatedPaymentsMember" abstract="true" name="InsuranceRelatedPaymentsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_DerivativeIncreaseDecreaseInNotionalAmountSingleInstrument" abstract="false" name="DerivativeIncreaseDecreaseInNotionalAmountSingleInstrument" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_AccruedAndOtherCurrentLiabilitiesMember" abstract="true" name="AccruedAndOtherCurrentLiabilitiesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_AccumulatedOtherComprehensiveIncomeLossNetOfTaxRollForward" abstract="true" name="AccumulatedOtherComprehensiveIncomeLossNetOfTaxRollForward" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
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  <xs:element id="lgn_A3.3750InterestRateSwapMaturingAtDecember2026Member" abstract="true" name="A3.3750InterestRateSwapMaturingAtDecember2026Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A4.0433InterestRateSwapMaturingAtDecember2026Member" abstract="true" name="A4.0433InterestRateSwapMaturingAtDecember2026Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A3.2480InterestRateSwapMaturingAtDecember2027Member" abstract="true" name="A3.2480InterestRateSwapMaturingAtDecember2027Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InterestRateSwapMaturesBetweenJanuary2024ToSeptember2025Member" abstract="true" name="InterestRateSwapMaturesBetweenJanuary2024ToSeptember2025Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InterestRateSwapMaturesBetweenSeptember2025ToDecember2026Member" abstract="true" name="InterestRateSwapMaturesBetweenSeptember2025ToDecember2026Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A0.8325InterestRateSwapMaturingAtJanuary2025Member" abstract="true" name="A0.8325InterestRateSwapMaturingAtJanuary2025Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A1.1740InterestRateSwapMaturingAtJanuary2025Member" abstract="true" name="A1.1740InterestRateSwapMaturingAtJanuary2025Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_A1.1732InterestRateSwapMaturingAtJanuary2025Member" abstract="true" name="A1.1732InterestRateSwapMaturingAtJanuary2025Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InterestRateSwapMaturesBetweenJanuary2023ToJanuary2025Member" abstract="true" name="InterestRateSwapMaturesBetweenJanuary2023ToJanuary2025Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InterestRateSwapMaturesBetweenFebruary12025ToDecember312026Member" abstract="true" name="InterestRateSwapMaturesBetweenFebruary12025ToDecember312026Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_LGNAUnitsMember" abstract="true" name="LGNAUnitsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_LGNBUnitsMember" abstract="true" name="LGNBUnitsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_CommonStockVotingRightsVotes" abstract="false" name="CommonStockVotingRightsVotes" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="lgn_ShareBasedPaymentArrangementFairValueAtModificationDateBasis" abstract="false" name="ShareBasedPaymentArrangementFairValueAtModificationDateBasis" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfVestingInstallments" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfVestingInstallments" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriod" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:sharesItemType"/>
  <xs:element id="lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedInPeriodWeightedAverageExercisePrice" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:perShareItemType"/>
  <xs:element id="lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExercisableWeightedAverageGrantDateFairValue" abstract="false" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExercisableWeightedAverageGrantDateFairValue" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types:perShareItemType"/>
  <xs:element id="lgn_LGNBUnitsExchangeableForClassACommonStockMember" abstract="true" name="LGNBUnitsExchangeableForClassACommonStockMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_TaxReceivableAgreementBasisSpreadOnVariableRatePercentage" abstract="false" name="TaxReceivableAgreementBasisSpreadOnVariableRatePercentage" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="dtr-types:percentItemType"/>
  <xs:element id="lgn_EngineeringConsultingMember" abstract="true" name="EngineeringConsultingMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_InstallationMaintenanceMember" abstract="true" name="InstallationMaintenanceMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types:domainItemType"/>
  <xs:element id="lgn_SelfInsuranceThresholdForStopLossInsurance" abstract="false" name="SelfInsuranceThresholdForStopLossInsurance" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_SuretyBondsOutstanding" abstract="false" name="SuretyBondsOutstanding" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" abstract="false" name="IncreaseDecreaseInCapitalExpendituresIncurredButNotYetPaid" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_DeferredOfferingCostsIncludedInAccountsPayable" abstract="false" name="DeferredOfferingCostsIncludedInAccountsPayable" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" abstract="false" name="DeferredOfferingCostsIncludedInAccruedAndOtherCurrentLiabilities" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" abstract="false" name="ContributionsFromParentIForSeriesAInterestsAndRestrictedSeriesCInterests" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_ContributionsFromParentIIForSeriesAInterests" abstract="false" name="ContributionsFromParentIIForSeriesAInterests" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_RightOfUseAssetModificationsForOperatingLeases" abstract="false" name="RightOfUseAssetModificationsForOperatingLeases" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_NonCashIPOAndCorporateReorganizationInformationAbstract" abstract="true" name="NonCashIPOAndCorporateReorganizationInformationAbstract" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="lgn_ReclassificationOfSeriesAInterestsAndRestrictedSeriesCInterestsFromLiabilityToEquity" abstract="false" name="ReclassificationOfSeriesAInterestsAndRestrictedSeriesCInterestsFromLiabilityToEquity" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_TaxReceivableAgreementLiabilityRecognized" abstract="false" name="TaxReceivableAgreementLiabilityRecognized" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="lgn_DeferredTaxAssetNetOfValuationAllowanceRecognizedInConnectionWithTheTaxReceivableAgreementLiability" abstract="false" name="DeferredTaxAssetNetOfValuationAllowanceRecognizedInConnectionWithTheTaxReceivableAgreementLiability" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
</xs:schema>
