From my limited perspective, there is one fundamental problem: how do you coordinate a payment between two nodes on the lightning network?

There are sovereign nodes and permissioned nodes. You're either trying to send a payment on your own keys or ask a sovereign to send a payment on your behalf. And the receiver is the same.

Now coming at it from the top, Nostr is a social graph among humans that lets you find people that you want to send payments to. The problem splits in two. How do people advertise their sovereign/permissioned lightning node in a way that other people can pay them reliably? And how can my Nostr client gain permission to use my node to pay an invoice it fetches from the receiver?