Few things:
- Federated Protocol essentially offers something similar to Peer-To-Peer communication like Bit Torrent, only that it's a server-to-server communication protocol. You could GDPR the Lemmy servers that are within the EU jurisdiction, but good luck enforcing that outside of EU.
- Anything you post in public is PUBLIC, this should be obvious and I honestly advise not to put your real name out there if you're not going to be responsible with your posting or behavior.
- Services like Internet Archive exists, so your stuff are going to be saved forever whether you like to or not.
If you're not comfortable with the non-compliance of GDPR on Lemmy Server, then I can suggest two things:
- Detach your real life identity from Lemmy and assume everything you do with that service/website is public.
- Find other platform that respects GDPR.