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Stock-Based Compensation (Details 10) (Stock Appreciation Rights [Member], USD $)
In Millions, except Per Share data, unless otherwise specified
 12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Outstanding awards, shares 1.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber 1.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
Exercisable, shares 1.0lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableNumber  
$28.24 to $36.935 [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Range of Exercise Prices per Share, lower range limit $ 28.24lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
Range of Exercise Prices per Share, upper range limit $ 36.94lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
Outstanding awards, shares 0.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
Outstanding awards, weighted-average remaining contractual term 4 years 3 months 20 days  
Outstanding awards, aggregate intrinsic value $ 22.3lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
Exercisable, shares 0.4lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
Exercisable, weighted-average remaining contractual term 4 years 1 month 5 days  
Exercisable, aggregate intrinsic value 17.6lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange1Member		  
$46.78 to $51.395 [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Range of Exercise Prices per Share, lower range limit $ 46.78lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
Range of Exercise Prices per Share, upper range limit $ 51.40lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
Outstanding awards, shares 0.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
Outstanding awards, weighted-average remaining contractual term 6 years 6 months 0 days  
Outstanding awards, aggregate intrinsic value 4.1lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
Exercisable, shares 0.1lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
Exercisable, weighted-average remaining contractual term 6 years 0 months 0 days  
Exercisable, aggregate intrinsic value 1.2lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange2Member		  
$81.105 to $81.14 [Member]    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Range of Exercise Prices per Share, lower range limit $ 81.105lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeLowerRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member		  
Range of Exercise Prices per Share, upper range limit $ 92.64lii_SharebasedCompensationSharesAuthorizedunderNonOptionEquityInstrumentPlansExercisePriceRangeUpperRangeLimit
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member		  
Outstanding awards, shares 0.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member		  
Outstanding awards, weighted-average remaining contractual term 3 years 1 month 5 days  
Outstanding awards, aggregate intrinsic value 33.2lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsOutstandingIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member		  
Exercisable, shares 0.5lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member		  
Exercisable, weighted-average remaining contractual term 3 years 1 month 5 days  
Exercisable, aggregate intrinsic value $ 33.2lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableIntrinsicValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
/ us-gaap_ShareBasedCompensationSharesAuthorizedUnderStockOptionPlansByExercisePriceRangeAxis
= lii_ExercisePriceRange3Member