Collaboration Agreement - Revenue Recognized Related to Each of the Performance Obligations and the Remaining Deferred Revenue (Details) $ in Thousands	6 Months Ended
Jun. 30, 2023 USD ($)
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Deferred revenue at December 31, 2022	$ 15,352
Revenue recognized	(868)
Deferred revenue at June 30, 2023	14,484
Combined Performance Obligation
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Deferred revenue at December 31, 2022	11,748
Deferred revenue at June 30, 2023	11,748
Development Activities Performance Obligation
Collaborative Arrangement and Arrangement Other than Collaborative [Line Items]
Deferred revenue at December 31, 2022	3,604
Revenue recognized	(868)
Deferred revenue at June 30, 2023	$ 2,736

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.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 808
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479402/808-10-50-1

+ Details

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

- Definition

Amount of deferred income and obligation to transfer product and service to customer for which consideration has been received or is receivable.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(26)(c))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

Name:	us-gaap_DeferredRevenue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of revenue recognized that was previously reported as deferred or unearned revenue.

+ References

No definition available.

+ Details

Name:	us-gaap_DeferredRevenueRevenueRecognized1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Details

Name:	us-gaap_TypeOfArrangementAxis=lyra_CombinedPerformanceObligationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_TypeOfArrangementAxis=lyra_DevelopmentActivitiesPerformanceObligationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: