Cashu mint issues a bolt12 offer to cashu wallet.

Paying the offer is effectively paying the wallet.

Lightning to ecash: Alice pays 100 sats to Bob’s offer. Bob receives 100 esats from his mint.

Bob (cashu wallet) can give out the offer just as a lightning node would, but he never touches the LN, just ecash. Whenever Alice pays Bob’s offer, it appears like a normal lightning transaction.