Ah that's a much better way, and preferred all around. 

MinatoPay

bitcoin

Feature Release: Instant Withdrawals

Hey! What does "based on LNURL deposits" mean exactly? You send sats to the merchants using a LNURL-Pay link/Lightning Address?

If so, wouldn't it be possible to do some kind of "proxy" thing (like lnproxy.org or geyser.fund), where:
1. Customer hits "Pay" on checkout page
2. Minato gets an invoice for the required amount + Minato fees from the merchants self-custodial wallet using LNURL-Pay
3.  Minato crafts an invoice for the required amount and with the same payment hash as the invoice in step 2., and shows it to customer.
4. When customers pays invoice of step 3., Minato pays the initial invoice of step 2. in order to get the preimage, then can settle the customer-facing invoice (the one created in step 3.) using said preimage.

This way, Minato never takes custody of the funds. Minato can always fall back to the more classic custodial method if the merchants wallet is slow to respond, so that the customer's experience remains fast.