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.
Do Lemmy instances not scale horizontally?
In theory, they can. But it depends on how it's deployed.
From my cursory look at the deployment docs, Lemmy's default deployment option is via docker. It relies on a postgreSQL server, which may or may not scale horizontally depending on the admin's choice of implementation. For example, a deployment on AWS using Aurora would theoretically utilize auto-scaling.
I haven't personally deployed an instance so, grain of salt.
EDIT: A good discussion about DB scaling here: https://github.com/LemmyNet/lemmy/issues/3005
They do, but I'm not sure how well, I'm not a dev, and have no programming knowledge, so looking at the documentation looks like arcane hieroglyphs.
I'm pretty sure I read a comment about it from one of the devs, but can't recall the fine details of the conversation.