I don't think the Lighning Network will help Litecoin that much in gaining more unique users. I see LTC as something like a testnet for Bitcoin, and a very good one. If Segwit and LN is proven good and running well in LTC, I think we might see more and more miners slowly activating Segwit. And if it does activate, LTC's technical advantage is nullified.
Yeah. Litecoin would really serve its purpose as a testing ground for Bitcoin, to have an idea of what to expect in the future if Bitcoin adopts it too. As the LTC network is much smaller than Bitcoin's, it achieved consensus at a quicker rate than its counterpart, leaving the path towards the activation of SegWit.
The good side about this, is that now Litecoin would be much faster and capable to handle more transaction throughput than Bitcoin, when the block size increases over time, not to mention that it solves a very important flaw such as transaction malleability.
Nevertheless, while the future of Litecoin is uncertain, one thing for sure is that it will survive alongside Bitcoin for many years to come. Just my thoughts.