It's not really possible as long as Lemmy is a website. E2EE works on Matrix because it's an app, and therefore it can manage your encryption keys in ways a browser cannot do for you. (You can save things in the client, but not in a reliable enough way for something like the master key for every communication you ever had that if you lose you get locked out of all your chat history.) In the case of Lemmy, the signing keys for your federated actions are handled by the server, which is perfectly fine for 99% of what you use Lemmy for (public posts and comments), but it also means that even if they implemented E2EE for chats, the keys to decrypt the convo would be right on the same server.

That's why Lemmy actively pushes you to set up a Matrix account, because Matrix makes better tradeoffs for the purposes of messaging, while Lemmy's tradeoffs are more relevant to a link aggregator style social media.