lightning channels are an on-chain transaction shared between two peers. by default both usually have to be online because usually there is a policy to auto-close the channel if the other peer is offline for a substantial amount of time.
however, if two nodes decided to allow it, i'm pretty sure it can be done, just that you can't do any transactions without them both being online to share an update to the transaction that changes the balance.
So that's another way it's not self custody
it's self custody that requires two selves lol
it's got the same level of trust though. the protocol makes it so that the worst case scenario you have to pay a bitcoin transaction fee to close the channel.
in comparison, an ecash token is completely worthless if the mint goes down or refuses to pay you via lightning or onchain when you try to redeem it. an exchange wallet is exactly the same in this respect. in fact there is very little difference between an exchange wallet and an ecash token. different authentication mechanism but it's the same trust me bro.
But I don't have to pay any fees to hold Bitcoin because it's self custody
