Simply put SegWit will make it possible to Steal BTC Value to use in LN Alternative Payment System using BTC IOUs .
Miners will lose money because LN can decrease the number of OnChain Transactions.
(In Theory : Using advanced features LN may even allow only certain miners to process the transaction Fees when Onchain BTC Transactions are required.)
The only thing LN does is limit fees for miners and give those fees to owners of Lightning Network (Blockstream)