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Stock-Based Compensation (Details 1) (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]
Payout ratio for shares paid 100.00%lii_PayoutPercentage    
Performance Shares [Member]      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Compensation expense $ 11.5us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 17.1us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 5.7us-gaap_AllocatedShareBasedCompensationExpense
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
Weighted-average fair value of grants, per share $ 88.26us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 78.00us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
$ 48.64us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
Payout ratio for shares paid 153.20%lii_PayoutPercentage
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
86.90%lii_PayoutPercentage
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
52.50%lii_PayoutPercentage
/ us-gaap_AwardTypeAxis
= us-gaap_PerformanceSharesMember
[1] Stock-Based compensation expense was recorded in our Corporate and other business segment.