Iirc there are a few lightning network clients that function on top of bitcoin core (I don't know if they share wallets or not but I'd assume they don't).
There are few client which depends on Bitcoin Core (such as LND and Core Lightning). But i don't expect any of those use Bitcoin Core wallet since it can't store LN-related data (e.g. channel state, LN transaction/routing history). At very least, i'm sure Core Lightning has it's own internal wallet.
They do not have to have both LN and layer 1 BTC. There are some wallets that are only LN. But the majority of LN wallets do support on chain too.
Isn't it a confirmation that we need an intermediary wallet to use the lightning network? In other words, there's no direct access, but we must necessarily use a bridge whenever we want to switch from one to the other. So, there's waters between the layers. Is it correct?
Wrong, no intermediary/bridge is needed unless you use third-party or custodial service.
