Are there any conditions or situations that prevent a player from choosing to be lead investigator?
The rulebook states:


  At the end of each Mythos Phase, the Lead Investigator may pass the Lead Investigator token to any player of his choice.


Therefore no, according to the rules.

As an added point. If the Lead investigator wanted to pass it to a dead character this would happen:


  If the defeated investigator has the Lead Investigator token, he must pass the token to an investigator of his choice.


But since New Investigators are chosen at the end of the Mythos phase as well you could always ensure that New Investigator choice takes precedence to prevent any chance of the dead player being left out.