Mortgages Payable and Debt Maturities - Summary of Debt Obligation and Interest Rate Derivatives (Detail) $ in Thousands	Mar. 31, 2023 USD ($)
Debt Instrument [Line Items]
Payables due 2023	$ 3,801
Payables due 2024	197,465
Payables due 2025	6,093
Payables due 2026	600,107
Payables due 2027	1,069,000
Payables due Thereafter	1,550,000
Debt obligations	3,426,466
Line of credit - variable rate SOFR + 0.775% (5.68% at March 31, 2023)
Debt Instrument [Line Items]
Payables due 2027	619,000
Debt obligations	619,000
Debt instrument, fair value	619,000
Term Note - Fixed Rate 4.533% [Member]
Debt Instrument [Line Items]
Payables due 2024	175,000
Debt obligations	175,000
Term note, fair value	170,785
Term Note - Fixed Rate 3.50% [Member]
Debt Instrument [Line Items]
Payables due 2026	600,000
Debt obligations	600,000
Term note, fair value	567,557
Term Note - Fixed Rate 3.875% [Member]
Debt Instrument [Line Items]
Payables due 2027	450,000
Debt obligations	450,000
Term note, fair value	423,097
Term Note - Fixed Rate 3.67% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	200,000
Debt obligations	200,000
Term note, fair value	183,277
Term Note - Fixed Rate 4.00% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	350,000
Debt obligations	350,000
Term note, fair value	322,533
Term Note - Fixed Rate 2.20% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	400,000
Debt obligations	400,000
Term note, fair value	316,610
Term note - fixed rate 2.40% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	600,000
Debt obligations	600,000
Term note, fair value	462,816
Mortgage Note - Fixed Rate 5.26% [Member]
Debt Instrument [Line Items]
Payables due 2023	3,544
Debt obligations	3,544
Term note, fair value	3,502
Mortgage Note - Fixed Rate 4.4625% [Member]
Debt Instrument [Line Items]
Payables due 2024	22,105
Debt obligations	22,105
Term note, fair value	20,943
Mortgage Note - Fixed Rate 4.44% [Member]
Debt Instrument [Line Items]
Payables due 2023	94
Payables due 2024	131
Payables due 2025	5,850
Debt obligations	6,075
Term note, fair value	5,798
Mortgage Note - Fixed Rate 5.99% [Member]
Debt Instrument [Line Items]
Payables due 2023	163
Payables due 2024	229
Payables due 2025	243
Payables due 2026	107
Debt obligations	742
Term note, fair value	$ 741

Long term debt maturities repayments of principal after year four.

No definition available.

Name:	lsi_LongTermDebtMaturitiesRepaymentsOfPrincipalAfterYearFour
Namespace Prefix:	lsi_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Fair value portion of debt instrument payable, including, but not limited to, notes payable and loans payable.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI https://asc.fasb.org/extlink&oid=123594938&loc=d3e13433-108611

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1D
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495340-112611

+ Details

Name:	us-gaap_DebtInstrumentFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
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

No definition available.

+ Details

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

- Definition

Amount, excluding unamortized premium (discount) and debt issuance cost, of long-term debt. Excludes lease obligation.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 4
-Subparagraph (b)(3)
-URI https://asc.fasb.org/extlink&oid=123466204&loc=SL6031897-161870

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69C
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495737-112612

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(16))
-URI https://asc.fasb.org/extlink&oid=126734703&loc=d3e572229-122910

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 55
-Paragraph 69B
-URI https://asc.fasb.org/extlink&oid=123466577&loc=SL123495735-112612

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(16))
-URI https://asc.fasb.org/extlink&oid=126897435&loc=d3e534808-122878

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1D
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495340-112611

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(22))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1E
-Subparagraph (d)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495348-112611

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-URI https://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 10
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=123465755&loc=d3e1835-112601

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 20
-Section 50
-Paragraph 1E
-Subparagraph (d)
-URI https://asc.fasb.org/extlink&oid=123466505&loc=SL123495348-112611

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 470
-SubTopic 10
-Section 50
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=123465755&loc=d3e1835-112601

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-URI https://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of long-term debt payable, sinking fund requirement, and other securities issued that are redeemable by holder at fixed or determinable price and date, maturing in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-URI https://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

+ Details

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

- Definition

Fair value portion of notes payable.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.19,20,22)
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_LineOfCreditFacilityVariableInterestRateSofrPlusZeroPointSevenSevenFivePercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateFourPointFiveThreeThreePercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateThreePointFiveZeroPercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateThreePointEightSevenFivePercentageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateThreePointSixSevenPercentageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateFourPointZeroPercentageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateTwoPointTwoZeroPercentageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteFixedRateTwoPointFourZeroPercentageMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_MortgageNoteFixedInterestRateFivePointTwoSixPercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_MortgageNoteFixedInterestRateFourPointFourSixTwoFivePercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_MortgageNoteFixedInterestRateFourPointFourFourPercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_MortgageNoteFixedInterestRateFivePointNinetyNinePercentMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: