Sounds fantastic, where can I learn more about the project? Make sure to join our R&D chat: https://t.me/CashuBTC

To your question: in principle, the mint could run a service that hosts a Lightning address and pushes a Cashu token to the client's inbox. Since the receiver is supposed to be offline, it would equal a payment from the sender to the mint (LN) and a payment from the mint to the client (Ecash).

A more sophisticated approach could be that the client deposits a bunch of pre-generated BlindedMessages with the mint + LN address server and those are then signed when the LN payment arrives (we call this a "blank output"). That way, you also preserve the privacy for the ecash and skip the mint->receiver payment.