Lines of Credit and Financing Arrangements (Outstanding Debt Obligations) (Details) - USD ($) $ in Millions	Dec. 31, 2020	Dec. 31, 2019
Current maturities of long-term debt:
Finance lease obligations	$ 10.1	$ 7.8
Domestic credit facility	9.9	321.9
Long-Term Debt:
Finance lease obligations	29.3	25.9
Total long-term debt	970.7	849.3
Debt Issuance Cost, Gross, Noncurrent	(8.6)	(2.1)
Total debt	980.6	1,171.2
Domestic Credit Facility [Member]
Current maturities of long-term debt:
Domestic credit facility	0.0	30.0
Debt issuance costs	(0.2)	(0.9)
Long-Term Debt:
Total long-term debt	0.0	475.5
Asset Securitization [Member]
Current maturities of long-term debt:
Finance lease obligations	0.0	285.0
Senior Unsecured Notes [Member]
Long-Term Debt:
Total long-term debt	$ 950.0	$ 350.0

Amount of capital lease obligation due within one year or the normal operating cycle, if longer.

Reference 1: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121569800&loc=d3e45023-112735

Reference 2: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121616839&loc=d3e45280-112737

Reference 3: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(19))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount equal to the present value (the principal) at the beginning of the lease term of minimum lease payments during the lease term (excluding that portion of the payments representing executory costs such as insurance, maintenance, and taxes to be paid by the lessor, together with any profit thereon) net of payments or other amounts applied to the principal, through the balance sheet date and due to be paid more than one year (or one operating cycle, if longer) after the balance sheet date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-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

Reference 2: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121616839&loc=d3e45280-112737

Reference 3: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 840
-SubTopic 30
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121569800&loc=d3e45023-112735

+ Details

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

- Definition

Amount of short-term and long-term debt and lease obligation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.13,16)
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

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 210.7-03.16)
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

+ Details

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

- Definition

Amount, before accumulated amortization, of debt issuance costs classified as current. Includes, but is not limited to, legal, accounting, underwriting, printing, and registration costs.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-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

+ Details

Name:	us-gaap_DeferredFinanceCostsCurrentGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, before accumulated amortization, of debt issuance costs classified as noncurrent. Includes, but is not limited to, legal, accounting, underwriting, printing, and registration costs.

+ 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 210.5-02.17)
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-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

+ Details

Name:	us-gaap_DeferredFinanceCostsNoncurrentGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of long-term debt and lease obligation, classified as noncurrent.

+ References

+ Details

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

- References

No definition available.

+ Details

Name:	us-gaap_LongTermDebtAndCapitalLeaseObligationsAbstract
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, classified as current. Includes, but not limited to, notes payable, bonds payable, debentures, mortgage loans and commercial paper. Excludes capital lease obligations.

+ References

+ Details

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

- References

No definition available.

+ Details

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

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_DomesticLineOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=lii_AssetSecuritizationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_SeniorNotesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: