Which functionality is enabled with Segwit that LTC is not able to provide today?
I can understand somewhat the reasoning for Bitcoin, Segwit makes LN possible to scale Bitcoin. it can be argued whether larger blocks is better.
Segwit makes no good sense for LTC, blocks aren't filled and not going to be filled for years. So what functionality?
It enables cross chain transactions so you could have fully decentralised exchanges, though I presume the other coins you're exchanging would need it too. I believe dealing with the malleability thing also enables viable smart contracts.
And even if there isn't a capacity problem, a Lightning Network opens up possibilities with proper micropayments and maybe machine to machine stuff as well. Even a 1c fee and 2.5 minute wait is too much for some things.
It would all still largely be pie in the sky stuff. I'm not convinced how many people would choose to trust a smart contract for anything beyond piffling things, and LNs might turn out to be a right mess, but at least the possibility would be out there.