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Compensatory Equity Incentive Plan and Other Equity Incentives (Details 4) (USD $)
9 Months Ended
Mar. 31, 2015
Stock Options  
Granted 103,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
Balance ending, shares unexercisable and unvested 224,500us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares
Restricted Stock Units  
Balance, ending, shares unexercisable/unvested 403,870us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
Class A Common Stock [Member]  
Total Shares  
Beginning Balance 547,303lpth_SharebasedCompensationArrangementBySharebasedPaymentAwardSharesNonvestedNumberOfShares
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Granted 322,000lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesGrantsInPeriodGross
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Vested (240,933)lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestedInPeriodGross
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Balance ending 628,370lpth_SharebasedCompensationArrangementBySharebasedPaymentAwardSharesNonvestedNumberOfShares
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Weighted Average Grant Date Fair Values (per share)  
Beginning Balance 1.18lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Granted 1.36lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardsGrantsInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Vested 1.32lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardVestedInPeriodWeightedAverageGrantDateFairValue
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Ending Balance 1.23lpth_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonvestedWeightedAverageGrantDateFairValue
/ us-gaap_StatementEquityComponentsAxis
= us-gaap_CommonClassAMember
Stock Options [Member]  
Stock Options  
Beginning Balance 193,000us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares
/ us-gaap_AwardTypeAxis
= us-gaap_StockOptionMember
Granted 103,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
/ us-gaap_AwardTypeAxis
= us-gaap_StockOptionMember
Vested (71,500)us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedNumberOfShares
/ us-gaap_AwardTypeAxis
= us-gaap_StockOptionMember
Balance ending, shares unexercisable and unvested 224,500us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares
/ us-gaap_AwardTypeAxis
= us-gaap_StockOptionMember
Restricted Stock Units [Member]  
Restricted Stock Units  
Beginning Balance 354,303us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Granted 219,000us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Vested (169,433)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember
Balance, ending, shares unexercisable/unvested 403,870us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
/ us-gaap_AwardTypeAxis
= us-gaap_RestrictedStockUnitsRSUMember