Short answer...yes but it may not need to. Lightning was originally envisioned for BTC and the tech behind LTC is very similar to BTC.
If this interests you I would really encourage you to read this post
https://steemit.com/cryptocurrency/@digicrypt/litecoin-what-you-need-to-know
It talks a lot about how LTC can be used as an experimental area for Bitcoin. I also talk in more detail about this in my most recent interview with Rogue Money.
I am also of the opinion however, that Bitcoin, while Lighting could be feasible and desirable, may not need it to scale. There are several solutions although not many as robust as this.