Litecoin is an altcoin created for faster transactions. It has no difference with bitcoin, but this. Since we are trying to increase the speed of the transaction's confirmation with the lightning network, I don't know if litecoin should be useful anymore.
Lightning network is faster to do off chain transactions, while litecoin does on chain transactions.
Litecoin is not a "faster" btc. It has some different proposals:
Lite coin uses other cryptographic algorithms. It does not use SHA-256, but Scrypt.
Scrypt algorithm cannot be effeciently mined using ASICS, so miners uses different hardware (more GPU/CPU).
Litecoin has a very small blocktime, 2.5 minutes while btc has 10 minutes. It also has much more coins in circulation.. it is a different project. If it survived until now, I don't see why lightning would have such a high impact in it.