What do you need from the CLF for such a service?
An A or CNAME record.
What sort of CNAME would you want?
I'd probably let the community decide the name, though mastodon|fediverse|etc.common-lisp.net come to mind. I can be pretty bad at naming things though, so I'm all ears for suggestions.
An example of what I'd run is at cons.ivy.io - I set it up this past weekend thinking that there was no interest from the CLF collectively. I still haven't changed much of the design and am absolutely open to suggestions about the design, graphics, etc.