Effect of ActivityPub, not Lemmy. All federating systems function similarly, because it's a feature of the protocol.
If instances want, they can ignore delete requests and your content stays in their cache forever (remember Pleroma nazis from couple of years ago?) - now, that is an instance problem that might be a GDPR issue, but good luck reporting it to anyone who cares. At best you can block and defederate, but that doesn't mean your posts are removed.
The fediverse has no privacy, it's "public Internet". Probably a good idea to treat it as such.