The conventional approach is to find some ways to do escrow.

You can't do that in a non custodial manner with LN yet.

But what have you don't need to?

Peer to peer Bitcoin to Fiat transaction needs escrow because that's a mismatch in transaction time and finality.

The finality mismatch will still be there, but with lightning the transaction time could be instantaneous.

So instead of escrowing Bitcoin until the Fiat payment has been confirmed, why can't we just do them simultaneously.

Now, physical lightning ATM fits this model perfectly, but is there a way to make it work with bank transfers?