This sort of challenge sounds like it needs an expert on TOGOM to tackle it.
Since Lois is at the DP with Lex on a date, would he trust Lois enough to tell her that he's not really dead? Lex might overhear and/or Lois might lose her cool. He might trust Perry or Jack, who could then suggest that his body be dragged out of the conference room so that they wouldn't have to be in there with a dead body. Then "Superman" could come along and save the day.
The only way I could see Clark resurrecting himself would be to claim Superman used some sort of Kryptonian medical machinery on his "spaceship" to bring Clark back to life. Unfortunately, since it was built for Kryptonians, not humans, using it on Clark busted the machine. <which is why he won't be able to use it on anyone else> Yes, I know, it's one big ol' whopper of lie, but Clark has been known to blur the truth to protect his secret identity.
