Yes.  A payment made on lightning is not visible on chain(although there are other more nuanced privacy concerns). This and proper on chain utxo management will help in the scenario you describe where you want privacy from the recipient of your payment and also helps privacy from 3rd party chain observers.

ChrisS

bitcoin

Would a triple maxi scenario scare you a little bit?

stack_harder

i use lightning where i can and for smaller amounts etc, but is the idea that by moving form chain to lightning and then making a payment, a would-be chain watcher would at least find it a lot harder to identify your remaining stack?
