No. Lemmy and Mastodon are unrestricted by design. Assume that any post on either service is public knowledge for any company to store and reuse for whatever purpose they see fit. Edits are not guaranteed to make it and deleting comments doesn’t even work within Lemmy, let alone outside on the wider Fediverse, so assume data redaction is impossible to execute perfectly.

You can try to block Threads all you want, but anyone, including Meta, can set up a server with a generic domain name, some fake user accounts, follow a couple million people and just hoover up all the posts on the Fediverse. In fact, some sketchy data broker you’ve never heard of (that knows where you live) is probably already doing that. You can try to set your Mastodon to require approving followers, but the server admins of any approved follower will still receive the message, and they can do with it whatever they want.

There are apps out there that leverage encryption to ensure that nothing becomes readable outside of its designated audience (barring an approved member getting hacked or turning out to be a dick), like Circles, but they don’t have mainstream appeal.

If you care about privacy, ownership of your work, or tracking, leave Lemmy and Mastodon, and avoid anything implementing ActivityPub. The protocol was designed not to keep any of these things in mind.