Mortgages Payable and Debt Maturities - Summary of Debt Obligation and Interest Rate Derivatives (Detail) $ in Thousands	Mar. 31, 2021 USD ($)
Debt Instrument [Line Items]
Payables due 2021	$ 376
Payables due 2022	519
Payables due 2023	50,533
Payables due 2024	197,985
Payables due 2025	6,077
Payables due Thereafter	2,000,106
Debt obligations	2,255,596
Line of credit - variable rate LIBOR + 0.95% (1.06% at March 31, 2021) [Member]
Debt Instrument [Line Items]
Payables due 2023	43,000
Debt obligations	43,000
Debt instrument, fair value	43,000
Term Note - Fixed Rate 4.533% [Member]
Debt Instrument [Line Items]
Payables due 2024	175,000
Debt obligations	175,000
Term note, fair value	195,252
Term Note - Fixed Rate 3.50% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	600,000
Debt obligations	600,000
Term note, fair value	657,471
Term Note - Fixed Rate 3.875% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	450,000
Debt obligations	450,000
Term note, fair value	494,057
Term Note - Fixed Rate 3.67% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	200,000
Debt obligations	200,000
Term note, fair value	215,203
Term Note - Fixed Rate 4.00% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	350,000
Debt obligations	350,000
Term note, fair value	394,261
Term Note - Fixed Rate 2.20% [Member]
Debt Instrument [Line Items]
Payables due Thereafter	400,000
Debt obligations	400,000
Term note, fair value	376,052
Mortgage Note - Fixed Rate 4.065% [Member]
Debt Instrument [Line Items]
Payables due 2021	79
Payables due 2022	108
Payables due 2023	3,620
Debt obligations	3,807
Debt instrument, fair value	3,936
Mortgage Note - Fixed Rate 5.26% [Member]
Debt Instrument [Line Items]
Payables due 2021	60
Payables due 2022	83
Payables due 2023	3,567
Debt obligations	3,710
Debt instrument, fair value	3,983
Mortgage Note - Fixed Rate 4.4625% [Member]
Debt Instrument [Line Items]
Payables due 2024	22,620
Debt obligations	22,620
Debt instrument, fair value	23,317
Mortgage Note - Fixed Rate 4.44% [Member]
Debt Instrument [Line Items]
Payables due 2021	92
Payables due 2022	125
Payables due 2023	130
Payables due 2024	136
Payables due 2025	5,833
Debt obligations	6,316
Debt instrument, fair value	6,765
Mortgage Note - Fixed Rate 5.99% [Member]
Debt Instrument [Line Items]
Payables due 2021	145
Payables due 2022	203
Payables due 2023	216
Payables due 2024	229
Payables due 2025	244
Payables due Thereafter	106
Debt obligations	1,143
Debt instrument, fair value	$ 1,244

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/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-URI http://asc.fasb.org/extlink&oid=121572278&loc=d3e13433-108611

+ 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, after unamortized (discount) premium and debt issuance costs, of long-term debt. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ 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 http://asc.fasb.org/extlink&oid=120520924&loc=SL6031897-161870

Reference 2: 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 http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 3: 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 http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

Reference 4: 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 http://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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 235
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04.(a))
-URI http://asc.fasb.org/extlink&oid=120395691&loc=d3e24072-122690

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 http://asc.fasb.org/extlink&oid=6802200&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

+ 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

+ 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 http://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_LineOfCreditFacilityVariableInterestRateLiborPlusZeroPointNineFivePercentMember
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_MortgageNoteFixedInterestRateFourPointZeroSixFivePercentMember
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: