Sale Of Stock, Number Of Shares Issued In Transaction, Exchanged Shares

No definition available.

Name:	lgn_SaleOfStockNumberOfSharesIssuedInTransactionExchangedShares
Namespace Prefix:	lgn_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Sale Of Stock Option Period

+ References

No definition available.

+ Details

Name:	lgn_SaleOfStockOptionPeriod
Namespace Prefix:	lgn_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Shares During Offering Period, Per Employee

+ References

No definition available.

+ Details

Name:	lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseSharesDuringOfferingPeriodPerEmployee
Namespace Prefix:	lgn_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Share-based Compensation Arrangement By Share-based Payment Award, Maximum Purchase Value During Offering Period, Per Employee

+ References

No definition available.

+ Details

Name:	lgn_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumPurchaseValueDuringOfferingPeriodPerEmployee
Namespace Prefix:	lgn_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Number of shares of equity interest issued or issuable by acquirer as part of consideration transferred in business combination.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479328/805-10-50-8

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 41
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-41

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-2

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479581/805-30-50-1

Reference 5: http://www.xbrl.org/2003/role/exampleRef
-Topic 805
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 42
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479303/805-10-55-42

+ Details

Name:	us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Aggregate number of common shares reserved for future issuance.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_CommonStockCapitalSharesReservedForFutureIssuance
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The number of shares issued or sold by the subsidiary or equity method investee per stock transaction.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 28
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-28

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(g)(1)(ii))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Topic 323
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481687/323-10-50-3

+ Details

Name:	us-gaap_ScheduleOfEquityMethodInvestmentsLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The highest percentage of annual salary that an employee is permitted to utilize with respect to the plan.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumEmployeeSubscriptionRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Purchase price of common stock expressed as a percentage of its fair value.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-4

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of shares issued during the period as a result of the conversion of convertible securities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(30))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_EmployeeStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_BusinessAcquisitionAxis=lgn_Total2026AcquisitionsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=lgn_SecondaryOfferingMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Stockholders' Equity (Details) - USD ($) $ / shares in Units, $ in Thousands				3 Months Ended
	Apr. 09, 2026	Feb. 25, 2026	Jan. 08, 2026	Mar. 31, 2026
Employee Stock
Schedule of Equity Method Investments [Line Items]
Common stock reservation of shares (in shares)		1,580,053
Eligible employees contribution percentage		15.00%
Maximum annual cash payments		$ 25
Maximum purchase shares during offering period		1,000
Purchase price of common stock, percent		90.00%
Total 2026 Acquisitions
Schedule of Equity Method Investments [Line Items]
Number of issued (in shares)				2,701,003
Common Class A
Schedule of Equity Method Investments [Line Items]
Exchanged shares (in shares)			780,121
Common Class A \| Common Stock
Schedule of Equity Method Investments [Line Items]
Exchange of Class B Common Stock to Class A Common Stock (in shares)				780,121
Common Class A \| Subsequent Event \| Common Stock
Schedule of Equity Method Investments [Line Items]
Exchange of Class B Common Stock to Class A Common Stock (in shares)	9,528,699
Common Class A \| Over-Allotment Option
Schedule of Equity Method Investments [Line Items]
Sale of stock option period			30 days
Number of shares issued (in shares)			1,260,326
Common Class A \| Over-Allotment Option \| Subsequent Event
Schedule of Equity Method Investments [Line Items]
Number of shares issued (in shares)	2,007,927
Common Class A \| Secondary Offering \| Subsequent Event
Schedule of Equity Method Investments [Line Items]
Number of shares issued (in shares)	15,394,112
Sale of stock, price (in dollars per share)	$ 54.00