Income Taxes (Schedule of Effective Income Tax Rate Reconciliation) (Details)	12 Months Ended
Dec. 31, 2023	Dec. 31, 2022
Income Tax Disclosure [Abstract]
Income tax computed at federal statutory tax rate	21.00%	21.00%
Permanent differences	(2.10%)	(1.40%)
State taxes, net of federal benefit	6.70%	4.90%
Research and development and other tax credits	5.20%	4.40%
Change in deferred tax asset valuation allowance	(31.00%)	25.80%
Loss of Attributes - IRC 382 Ownership Change	0.50%	(54.70%)
Other	(0.30%)

Effective income tax rate reconciliation ownership change.

No definition available.

Name:	lyra_EffectiveIncomeTaxRateReconciliationOwnershipChange
Namespace Prefix:	lyra_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(h)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480678/235-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to changes in the valuation allowance for deferred tax assets.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 6.I.Fact.4)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479360/740-10-S99-1

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to statutory income tax expense (benefit) outside of the country of domicile.

+ References

+ Details

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

- Definition

Percentage of the difference, between reported income tax expense (benefit) and the expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations, that is attributable to tax exempt income, equity in earnings (loss) of an unconsolidated subsidiary, minority interest income (expense), tax holiday, disposition of a business, disposition of an asset, repatriation of foreign earnings, repatriation of foreign earnings jobs creation act of 2004, change in enacted tax rate, prior year income taxes, change in deferred tax asset valuation allowance, and other adjustments.

+ References

No definition available.

+ Details

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

- Definition

Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

+ References

+ Details

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

- Definition

+ References

+ Details

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

- References

No definition available.

+ Details

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