I see where you're going with this. Yes, with a custom extension of the protocol, a mint should be able to do this. It's unusually that the mint produces wash by itself (it's an interactive process), so the mint would use something like their own wallet to do so. This is usually a no go for privacy reasons but since it's a locked token anyway and the receiver's pubkey will eventually be doxed upon redemption, the mint could mint those tokens itself.

I still think this doesn't embrace the potential ecash could bring to the whole process though, it would be a better strategy to make few LN payments but many ecash payments. But if it's worth considering because of existing support for keysend assuming it's easy to extend (tlv including relay+receiver npub), it might be worth exploding.