This site is currently struggling to handle the amount of new users. I have already upgraded the server, but it will go down regardless if half of Reddit tries to join.
However Lemmy is federated software, meaning you can interact seamlessly with communities on other instances like beehaw.org or lemmy.one. The documentation explains in more detail how this works. Use the instance list to find one where you can register. Then use the Community Browser to find interesting communities. Paste the community url into the search field to follow it.
You can help other Reddit refugees by inviting them to the same Lemmy instance where you joined. This way we can spread the load across many different servers. And users with similar interests will end up together on the same instances. Others on the same instance can also automatically see posts from all the communities that you follow.
Edit: If you moderate a large subreddit, do not link your users directly to lemmy.ml in your announcements. That way the server will only go down sooner.
Correct the performance problem now is all from local users (visiting lemmy.ml in their browser or app).
If lemmy.ml goes down, other instances still have full mirrors of them. Users there can interact with their local mirror as usual, and other users can see those interactions. However these would not be federated to other instances (lemmy.ml is responsible for announcing community posts to followers). However federated actions are retried a few times so it might federate later.