A receiver on the lightning network doesn't even know what lightning node sent the transaction. As far as a LN receiver is concerned, there is no mint on the senders node. Ecash adds no privacy benefits there.

The LN receiver doesn't know you have a mint. It doesn't know who the user(s) are. MINTS ARE FOR PROVIDING PRIVACY FOR USERS OF THE MINT FROM THE MINT OPERATOR. Not privacy to someone paid over lightning from the mint. Having a mint or not does not change the lightning transaction being sent. It only obfuscates who initiated the txn from the sending node operator.

And back to my original point, anyone using your mint and holding your ecash has an IOU from you for sats that you can choose to not honor. That is the risk of mints. If you are the only person using your mint, on your node, you are doing nothing for your privacy.