I've completely revamped the lives code. Haven't tested it yet (my desktop has just learned a cute little trick where it goes through a hard reboot if I run ZDoom) but hopefully I've got the knack for making sure each vital check has a direct causal link to some "objective" event that's unlikely to desync.
And, incidentally, I've fixed a crapton of the old bugs with the system - killing off the other players can actually end a deathmatch game with the no exit dmflag on now!Courtesy download link
EDIT: Nope, lives system is still shot. Good news is I think I've narrowed down why - I still haven't gotten around the obstacle of imposing player 0's cvar on everyone else. Having everyone set the cvar seems to work, though, but I suspect this would have worked even before I revamped the code.
There seems to be a bug where the wipeout sequence doesn't kick in if the second-last person to die doesn't respawn until the last person has also died. I have no idea what causes this.