All depends. First step is always running your own lightning node (which the vast majority don't do). But even after that there are a lot of caveats. Here are a few links with the technical details:

bitcoinmagazine.com/technical/state-of-bitcoin-lightning-network-privacy

https://abytesjourney.com/lightning-privacy/

https://github.com/lnbook/lnbook/blob/develop/16_security_privacy_ln.asciidoc#attacks-on-lightning

https://lightningprivacy.com/en/introduction

"We identified 27,183 private channels, discovered hidden balances, and showed how a passive adversary can infer payment endpoints with very high probability."
https://arxiv.org/pdf/2003.12470.pdf