Strictly speaking, "LambdaMOO" is several things at once.
… MOO being a variety of MUD.
One may access LambdaMOO at lambda.moo.mud.org port 8888, either via telnet or your favorite MUD client.
Most of the information about the LambdaMOO site is within LambdaMOO (which has to do with why there was never an actual website for the longest time). You can connect as a guest and wander about, or request a character.
If you think the site might be down, the LambdaMOO status blog is where outages are reported as soon as possible, which, depending on circumstances, may not be as soon as one would like, but so be it. Since this page runs off of the same server host, it will likely also be down at such times, meaning you will need to bookmark the status log if this link is to be at all useful.
is documented in the current MOO Programmer's Manual.
The current version (1.8.4) running at the LambdaMOO site is available at github (main branch). Bugs/issues should be reported there.
Further discussion, including development plans and various test suites, is available on my MOO server resources page.
The ancient FTP site, ftp://ftp.lambda.moo.mud.org/pub/MOO/ no longer runs since nobody uses FTP anymore. That content, including the latest LambdaCore extraction is now here instead.
--Rog