Inventories (Details) - USD ($) $ in Millions	12 Months Ended
Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Inventory Disclosure [Abstract]
Finished goods	$ 280.1	$ 402.9
Work in process	6.5	6.0
Raw materials and repair parts	207.8	198.8
Total	494.4	607.7
Excess of current cost over last-in, first-out cost	(55.0)	(63.6)
Total inventories, net	439.4	544.1
Pre-tax income (loss) from LIFO inventory liquidations	0.7	0.2	$ 0.0
Reserve balance obsolete and slow moving inventories	$ 24.6	$ 19.2

reserve balance obsolete and slow moving inventories

No definition available.

Name:	lii_Reservebalanceobsoleteandslowmovinginventories
Namespace Prefix:	lii_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The effect of liquidating LIFO (last in first out) inventory layers on income.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 330
-SubTopic 10
-Section S99
-Paragraph 3
-Subparagraph (SAB Topic 11.F)
-URI http://asc.fasb.org/extlink&oid=27011343&loc=d3e100079-122729

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount before valuation and LIFO reserves of completed merchandise or goods expected to be sold within one year or operating cycle, if longer.

+ 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 210.5-02.6(a)(1))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Gross amount, as of the balance sheet date, of merchandise, goods, commodities, or supplies held for future sale or to be used in manufacturing, servicing or production process.

+ 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 210.5-02.6(a))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount by which inventory stated at last-in first-out (LIFO) is less than (in excess of) inventory stated at other inventory cost methods.

+ 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 210.5-02.6(c))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount after valuation and LIFO reserves of inventory expected to be sold, or consumed within one year or operating cycle, if longer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section 45
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=121566466&loc=d3e6676-107765

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02.6(a))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Gross amount of unprocessed materials to be used in manufacturing or production process and supplies that will be consumed.

+ 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 210.5-02.6(a)(4),(5))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

- Definition

Amount before valuation and LIFO reserves of merchandise or goods in the production process expected to be completed within one year or operating cycle, if longer.

+ 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 210.5-02.6(a)(3))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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