As an equal opportunity downer, I have to challenge Super's use of language here, this is not an asynchronous payment any more than the K1 in a LNURL-Withdraw link or trusted shitcoin swap is.

Since the receiver must come online to sweep the state, it's not asynchronous, it's a promise not unlike any centralized solution.

The internet does not work asynchronously, it works through re-attempts and re-signaling.