P2P you're really just distributing the risk of someone tying bitcoin to your identity, you are dealing with individual sellers so the transactions are distributed from different wallets, so it makes it harder to like to you.

You still need to do things like have multiple addresses for each transaction so you don't have outside links from different transactions since one bad incoming UTO or one bad spend could tie that all that stack to you, but P2P is a good start.

As for LN you can do P2P on a service like Robosats but you would need your own wallet, no sense buying on robosats and sending to a custodial wallet, who now has a record with an email and IP attached to it.