There is a known privacy issue in the #lightningNetwork, where an attacker can gain crucial insights about the recipient in a BOLT 11 invoice!
Check out lipa's Invoice Detective service to learn how much can be inferred just by examining a BOLT 11 invoice and leveraging some knowledge of the lightning network graph.
Invoice Detective can identify whether the payee is a user of a non-custodial wallet, custodial exchange, or something else.
The good news is that blinded paths and trampoline routing might improve receiver privacy a lot.