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Stock-Based Compensation (Details 9) (Stock Appreciation Rights [Member], USD $)
In Millions, except Per Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2014
Stock Appreciation Rights [Member]
   
Schedule of information on stock units    
Outstanding awards, beginning of period 1.8us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Outstanding, Weighted-Average Exercise Price per Share, beginning of period $ 45.58lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 56.20lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
Granted 0.2us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsGranted
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Granted, Weighted-Average Excercise Price per Share $ 92.64lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsGrantsinPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Exercised (0.5)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsExercised
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Exercised, Weighted-Average Exercise Price per Share $ 35.91lii_SharebasedCompensationArrangementsbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisesinPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Forfeited 0us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsForfeitures
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Forfeited, Weighted-Average Exercise Price per Share $ 0.00lii_SharebasedCompensationArrangementsbySharebasedPaymentAwardNonOptionEquityInstrumentsForfeituresinPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Outstanding awards, end of period 1.5us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Exercisable at end of year, shares 1.0lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableNumber
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
 
Exercisable at end of year, Weighted-Average Exercise Price per Share $ 43.65lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsExercisableWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember