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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.

The whole point of lightning was for bitcoin. It is one of many solutions for scaling and I expect to see lots of competition on this front.

Correct, Lightning was originally envisioned for BTC. I would agree that after LTC gets LN many others would seek to follow.

It was also pushed onto the LTC network for political reasons.

There are definitely politics within the crypto space, everyone likes to think it is a decentralized utopia(not knocking the tech, it is amazing, I love it, just being realistic) There are certainly politics involved and interests that are forces in the markets and the technological development. I am often more fascinated with the drama/politics that the tech itself.

The drama and politics is the consensus - the most beautiful part.

wise words

The bitcoin community needs to come to some agreement