That's matrix

You mean something like on Matrix.org?

I can't understand what you're asking. If you want server to server relays, that's IRC that has been around since the previous millenium. Matrix also has something like that. If you want single independent servers, that's regular chat rooms.

There's Shoot as a fediverse alternative to Discord.

Otherwise, as others have said, IRC, Matrix, or Teamspeak are worth looking into. Especially the latter got a major refresh at one point, so it's not the dinosaur you might expect from its age.

Perhaps it could potentially be forked from the already existing Lemmy?

I really don't see the point of turning a discussion forum into an instant messaging platform. Like, the requirements are completely different. You might as well start from square one than trying to transform one into the other.

I like how everyone in here is like, "that's (insert one of twelve completely different things)."

xmpp + fluux messenger (https://github.com/processone/fluux-messenger)

XMPP and Deltachat are federated (though not with each other). A person can self-host a server that can communicate with any other XMPP or Deltachat instance.

That's IRC dawg

That would be TeamSpeak

Irc?

Teamspeak or Mumble are another good alternitive

There's Sup being developed by dansup (the lead dev of Pixelfed). Did he stop the development?

I mean, it's not exactly a Discord alternative, but rather an attempt at instant messaging.

https://pixelfed.social/supapp

People should also stop trying to make Lemmy something else than just forums.