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Stock-based Compensation (Details 7) (USD $)
In Millions, except Per Share data, unless otherwise specified
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Compensation expense $ 23.3us-gaap_AllocatedShareBasedCompensationExpense [1] $ 29.3us-gaap_AllocatedShareBasedCompensationExpense [1] $ 15.2us-gaap_AllocatedShareBasedCompensationExpense [1]
Stock Appreciation Rights [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Compensation expense $ 4.8us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 5.4us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 4.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
Weighted-average fair value of grants, per share $ 19.55lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsGrantsinPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 18.76lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsGrantsinPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
$ 14.34lii_SharebasedCompensationArrangementbySharebasedPaymentAwardNonOptionEquityInstrumentsGrantsinPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_StockAppreciationRightsSARSMember
[1] Stock-Based compensation expense was recorded in our Corporate and other business segment.