I have learnt that Lightning Network is a Level 2 protocol that can work with many blockchains. It reduces fees and transaction times at the expense of some security.
it is second "layer" as in a layer that only works on top of another (main) layer which is the on chain bitcoin transactions. it is not for "many blockchains" instead it is designed and is working on top of bitcoin. but like many other things that bitcoin starts, other altcoins copy and run their own as they are doing now. that doesn't change the fact that LN is a network built for and on top of bitcoin.
But it also doesn't deny the fact LN could be used for many blockchain/cryptocurrency. It also opens possibility of doing atomic-swap and DEX on LN which is win-win scenario.