Nope, not dead. I used to have an article bookmarked which told what he'd been up to of late, but the computer upon which I'd done so suffered a S.M.E.F. -- all I can remember for sure is that he was teaching math at UC Santa Cruz as of early 2004 (and, I think, still the odd semester at Harvard, but don't quote me on that.)
For the heck of it,
here is a Tom Lehrer website containing lyrics to most of his songs and... other stuff. Do yourselves a favor: find and listen to a recording of "Poisoning Pigeons in the Park" -- you can thank me later.
Edit:
I'm not 100% sure this is the right article, but it seems to cover most of the same points as the one I mentioned above, so
here you are.