Yeah, something like cashu could be considered, but it would be better if this is non-custodial solution. Other options are LNURL-Pay with some custodial service, or BOLT12 where it somehow gets the confirmation from my LSP (my phone doesn't need to be online). Not sure if BOLT12 allows that?

If not, one could imagine a scheme where

- I'd send some pre-signed "transactions" or "amounts" to my LSP (but don't share "secret")

- The LSP can't spend them unless it gets the secret.

- When I'm buying the item from the seller, I show the secret to the seller (e.g. they scan a QR on my phone, or NFC tap)

- Seller's phone/POC calls my LSP with the secret and pulls appropriate money.

A modification for plus points - I could also use another selfhosted server that does this revealing of secrets for me and then calls the LSP on my behalf.