Can a player pass himself in NFL?

The QB being a receiver is used the classic Hook and Lateral play.

Though, on a hook-and-lateral, the target of the lateral pass doesn’t have to be an eligible receiver – unlike a forward pass, any member of the offense can legally receive a lateral, since it’s essentially an extended handoff.

I’m not sure that’s a good answer to the LeBron question. LeBron could not in fact legally throw a pass to himself unless he bounced it off another player or the rim (or possibly the backboard; I can’t be bothered to check right now). That applies to a lob/alley oop as well. And, if it was legal, NBA players would do it all the time- they’d be able to drive to the rim without actually having to dribble the whole way, making it much easier in some situations.

Mr. Perfect could throw a pass to himself:

Yeah, he was perfect at everything. Except his own drug tolerance.