Hum I’m not technical at all but I guess if you uses LNURL/lightning addresses you loose all your privacy because it’s a third party server which query the invoice to the recipient node, knowing de facto the pubkey of the payee. So if you don’t use a VPN at least, one can correlate your ID to who you paid so basically no privacy at all.

Plus they could even present you a fake invoice paying themselves if they wanted to, so you have to trust them to be honest, or check carefully the invoice before paying it.

But at least they never take custody of your funds.
This is what I believe but not perfectly sure.