Hi vishalbty.

That's a tricky one to explain in a comment because there is a long history to the Segwit2x debate. I'll do my best!

Basically Segwit2x refers to an agreement to upgrade Bitcoin with two improvements (1) Segregated Witness ("Segwit" for short) and (ii) an increase in the block size from 1MB to 2MBs ("2x"). Bitcoin ended up adopting the first (Segregated Witness) but never adopted the second (the increase in block size from 1MB to 2MB).

So now, when people talk about the "Segwit2x Hard Fork" - they are really just referring to the increase in the block size from 1MB to 2MBs (because Bitcoin has already adopted Segregated Witness). Hence the answer to your question is no, Segwit2x doesn't impact Lightning Network - Lightning Network only requires Segregated Witness so it already works on Bitcoin and doesn't need an increase in block size.

Check out this Fortune article if you want to read more, it's a dated article but I found it was useful when I was researching this topic back in October. Just remember this article was written before the Segwit2x was cancelled (and now it looks like it's coming back!).

Others - please feel free to help out by recommending more recent articles.