LN doesn't need a fork like Segwit, protocol is already ready for it. It is only implementation that we are waiting on.
As for segwit, Electrum and some other wallets and exchanges have already implemented it, it is just that many exchanges and Bitcoin Core wallet hasn't yet. I hope they will soon.
You can also give it a try, it's really interesting to see this happening. Yalls.org is fine now, but Starblocks has some network error, so if you want success you should avoid the coffe now and head for the articles
https://bitcointalksearch.org/topic/bitcoin-fee-problem-solved-lightning-transactions-test-it-yourself-now-2621873