Lemmy lets you sign up and use it without a lot of the linked identifiers that reddit requires, that can be tied to your real identity (so they can serve you targeted ads). These include things like IP addresses, your email address, browser or device fingerprint, phone number, etc.
The other privacy concern I can think of, is middle-men capturing passwords and text input, and IP addresses. As long as your server isn't using cloudflare (unfortunately many lemmy servers are), and you aren't using a closed-source app or web UI (unfortunately many users are), you're likely safe.
Of course the other comments are correct that this is a public platform that's distributed, so we have to assume nefarious agencies are scanning it, so you shouldn't say anything that could tie your account to your real identity. Its also probably a good idea to create new accounts every so often if you're the type of person who tends to leak that info.