If it was me, I'd keep the website up despite the lawsuit, tell XAI and Elon to go fuck themselves, with the following arguments:
1. Twitter, or whatever "X" is, is a publicly available website, and a non-signed ToS isn't valid and doesn't legally prevent me from viewing web pages which you've placed on the public internet.
2. Nitter doesn't store or copy Twitter material on servers, only acts as a third party front end pulling cocks through to users that request from the public Xhitter pages.
3. Even if, for the sake of argument, it did store Xhitter cocks, it's allowed for fair use purposes.
Then I'd countersue X Corp./XAI/SpaceX/Musk/whatever is most legally relevant in state court for filing a SLAPP lawsuit and possibly for harassment.
But based on past experience and knowledge about the Nitter creator, I'm fully expecting him to roll over, cuck out and have no balls here, as he has done before when he permanently "closed Nitter down" a year or two ago, then quietly rehosted it sometime later. But this advice and opinion is offered nonetheless.
I'm sure in worse case someone will just rehost the shit on Tor and then everyone can resume reading Twitter garbage without having to dox themselves to Elon to make an account. But in the meantime I'm just going to keep "X" blocked, deleted all my Nitter bookmarks and I strongly, strongly recommend everyone block "X". You can block the site in uBlock Origin, for example.