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.
None of these are requested by the market.
Decentralized exchanges have existed for years. 95% of traders go to centralized websites to trade. This is a fact. Recent example is bitsquare, not really popular. Heck, most users prefer to keep coins on centralized exchanges and services, this is after numerous examples of goxxing and years of persuading them not to do it. They do not bother to download a wallet to keep private keys by themselves. It's a joke. Nobody needs decentralized exchanges.
Malleability is a small issue, most exchanges have learned to deal with it and have dealt with it for years with no large concerns. Smart contracts... LOL, they have been a marketing gimmick for Ethereum and they still haven't got one useful case for them. Who wants them and why?
Micropayments have existed for years too, tip bots is micropayments built on centralized services. Can't say they are particularly popular or wanted by the market. Much less for LTC, nobody uses LTC.
Bottom line. Segwit for LTC is a pump and dump job.