Debt instrument discount interest rate percentage.

No definition available.

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- Definition

Debt instrument interest coverage ratio.

+ References

No definition available.

+ Details

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- Definition

Debt instrument leverage ratio percentage.

+ References

No definition available.

+ Details

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- Definition

Indenture covenant percentage on unencumbered assets.

+ References

No definition available.

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- Definition

Amount of amortization expense attributable to debt issuance costs.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
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-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 3
-URI http://asc.fasb.org/extlink&oid=119993939&loc=d3e28555-108399

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Balance Type:	debit
Period Type:	duration

- Definition

Percentage points added to the reference rate to compute the variable rate on the debt instrument.

+ References

No definition available.

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
-SubTopic 30
-Section 45
-Paragraph 2
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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Description of the frequency of periodic payments (monthly, quarterly, annual).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
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-Paragraph 1
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-Section 50
-Paragraph 3
-Subparagraph (c)
-URI http://asc.fasb.org/extlink&oid=75038535&loc=d3e64711-112823

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Data Type:	xbrli:stringItemType
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Period Type:	duration

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ References

+ Details

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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

No definition available.

+ Details

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Data Type:	xbrli:stringItemType
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- Definition

Date when the debt instrument is scheduled to be fully repaid, in CCYY-MM-DD format.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.22(a)(2))
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-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-URI http://asc.fasb.org/extlink&oid=117815213&loc=d3e19207-110258

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Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of payment greater than the preceding installment payments to be paid at final maturity date of debt.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount, after accumulated amortization, of debt discount.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 835
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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Gross amount of debt extinguished.

+ References

No definition available.

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The fee, expressed as a percentage of the line of credit facility, for the line of credit facility regardless of whether the facility has been used.

+ References

No definition available.

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Date the credit facility terminates, in CCYY-MM-DD format.

+ References

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

The effective interest rate at the end of the reporting period.

+ References

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of borrowing capacity currently available under the credit facility (current borrowing capacity less the amount of borrowings outstanding).

+ References

+ Details

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

- Definition

The interest rate applicable to the portion of the carrying amount of long-term borrowings outstanding as of the balance sheet date, including current maturities, which accrues interest at a rate subject to change from time to time.

+ References

+ Details

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Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The cash outflow paid to third parties in connection with debt origination, which will be amortized over the remaining maturity period of the associated long-term debt.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 15
-Subparagraph (e)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3291-108585

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Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The cash inflow during the period from additional borrowings in aggregate debt. Includes proceeds from short-term and long-term debt.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3255-108585

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The cash inflow from a borrowing with the highest claim on the assets of the entity in case of bankruptcy or liquidation (with maturities initially due after one year or beyond the operating cycle, if longer).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3255-108585

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The cash outflow for debt initially having maturity due after one year or beyond the normal operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 15
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3291-108585

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

- Details

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Balance Type:
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- Details

Name:	srt_RangeAxis=srt_MinimumMember
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- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SecuredDebtMember
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Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_SeniorTermNoteDueOctoberFifteenTwoThousandThirtyMember
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Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_UnsecuredDebtMember
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Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_SeniorTermNoteDueJuneFifteenTwoThousandTwentyNineMember
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Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_SeniorTermNoteDueDecemberFifteenTwoThousandTwentySevenMember
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Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=lsi_SeniorTermNoteDueJulyOneTwoThousandTwentySixMember
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Balance Type:
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- Details

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Name:	us-gaap_DebtInstrumentAxis=lsi_TermNoteDueAugustFiveTwoThousandTwentyOneMember
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- Details

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Balance Type:
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- Details

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Unsecured Line of Credit and Term Notes - Additional Information (Detail) - USD ($)								3 Months Ended		9 Months Ended		12 Months Ended
	Oct. 09, 2020	Sep. 23, 2020	Jun. 03, 2019	Dec. 07, 2017	Jul. 21, 2016	Jun. 20, 2016	Apr. 08, 2014	Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019	Dec. 31, 2011	Dec. 31, 2019
Debt Instrument [Line Items]
Amount available on unsecured revolving line of credit								$ 499,900,000		$ 499,900,000
Unamortized senior term note discount								6,940,000		6,940,000			$ 5,583,000
Underwriting discount and other offering expenses										3,480,000	$ 3,099,000
Amortization expense related to deferred debt issuance costs										$ 3,033,000	2,873,000
Maximum [Member]
Debt Instrument [Line Items]
Leverage ratio percentage										60.00%
Indenture covenant percentage on unencumbered assets										150.00%
Minimum [Member]
Debt Instrument [Line Items]
Interest coverage ratio on debt										150.00%
Secured Debt [Member] \| Maximum [Member]
Debt Instrument [Line Items]
Leverage ratio percentage										40.00%
Senior Term Note Due October 15, 2030 [Member] \| Unsecured Senior Notes [Member]
Debt Instrument [Line Items]
Debt instrument principal amount		$ 400,000,000
Debt instrument,maturity date		Oct. 15, 2030
Debt instrument stated interest rate		2.20%
Debt instrument percentage discount to par		0.476%
Debt instrument, interest payable description										Interest on the 2030 Senior Notes is payable semi-annually in arrears on each April 15 and October 15, commencing with April 15, 2021
Unamortized senior term note discount		$ 1,900,000
Underwriting discount and other offering expenses		3,500,000
Proceeds from senior notes, net		$ 394,600,000
Senior Term Note Due June 15, 2029 [Member] \| Unsecured Senior Notes [Member]
Debt Instrument [Line Items]
Debt instrument principal amount			$ 350,000,000
Debt instrument,maturity date			Jun. 15, 2029
Debt instrument stated interest rate			4.00%
Debt instrument percentage discount to par			0.524%
Debt instrument, interest payable description										Interest on the 2029 Senior Notes is payable semi-annually in arrears on each June 15 and December 15.
Unamortized senior term note discount			$ 1,800,000
Underwriting discount and other offering expenses			3,100,000
Proceeds from senior notes, net			$ 345,100,000
Senior Term Note Due December 15, 2027 [Member] \| Unsecured Senior Notes [Member]
Debt Instrument [Line Items]
Debt instrument principal amount				$ 450,000,000
Debt instrument,maturity date				Dec. 15, 2027
Debt instrument stated interest rate				3.875%
Debt instrument percentage discount to par				0.477%
Debt instrument, interest payable description										Interest on the 2027 Senior Notes is payable semi-annually in arrears on each June 15 and December 15.
Unamortized senior term note discount				$ 2,100,000
Underwriting discount and other offering expenses				4,000,000.0
Proceeds from senior notes, net				$ 443,900,000
Senior Term Note Due July 1, 2026 [Member] \| Unsecured Senior Notes [Member]
Debt Instrument [Line Items]
Debt instrument principal amount						$ 600,000,000
Debt instrument,maturity date						Jul. 01, 2026
Debt instrument stated interest rate						3.50%
Debt instrument percentage discount to par						0.553%
Debt instrument, interest payable description										Interest on the 2026 Senior Notes is payable semi-annually in arrears on each January 1 and July 1.
Unamortized senior term note discount						$ 3,300,000
Underwriting discount and other offering expenses						5,500,000
Proceeds from senior notes, net						$ 591,200,000
Term Note Due July 21, 2028 [Member]
Debt Instrument [Line Items]
Debt instrument,maturity date					Jul. 21, 2028
Debt instrument stated interest rate					3.67%
Additional secured term note					$ 200,000,000
Term Note Due April 8, 2024 [Member]
Debt Instrument [Line Items]
Debt instrument,maturity date							Apr. 08, 2024
Debt instrument stated interest rate							4.533%
Additional secured term note							$ 175,000,000
Term Note Due April 8, 2024 [Member] \| Maximum [Member]
Debt Instrument [Line Items]
Debt instrument stated interest rate							6.283%
Term Note Due August 5, 2021 [Member]
Debt Instrument [Line Items]
Debt instrument,maturity date												Aug. 05, 2021
Debt instrument stated interest rate												5.54%
Additional secured term note												$ 100,000,000
Term Note Due August 5, 2021 [Member] \| Subsequent Event [Member]
Debt Instrument [Line Items]
Repayments of term debt	$ 100,000,000
Debt instrument whole payment required as a result of paying off term note prior to its maturity	$ 4,000,000.0
Term Note Due August 5, 2021 [Member] \| Maximum [Member]
Debt Instrument [Line Items]
Debt instrument stated interest rate												7.29%
Senior Notes and Term Notes [Member]
Debt Instrument [Line Items]
Amortization expense related to deferred debt issuance costs								600,000	$ 600,000	$ 1,800,000	$ 1,700,000
Revolving Credit Facility [Member]
Debt Instrument [Line Items]
Revolving credit limit								$ 500,000,000		$ 500,000,000
Line of credit facility, expiration date										Mar. 10, 2023
Basis spread over LIBOR										0.95%
Facility fee										0.15%
Interest rate, line of credit facility								1.13%		1.13%			2.75%
Revolving Credit Facility [Member] \| Term Note Due June 4, 2020 [Member]
Debt Instrument [Line Items]
Debt instrument principal amount								$ 100,000,000		$ 100,000,000
Basis spread over LIBOR										1.00%
Debt instrument variable interest rate								1.18%		1.18%			2.80%
Principal amount paid off										$ 100,000,000
Revolving Credit Facility [Member] \| Term Note [Member]
Debt Instrument [Line Items]
Revolving credit limit								$ 900,000,000		$ 900,000,000