No one says they get a lifetime claim, just that some cannot be legally fired without cause. Not sure why you are going to the extreme of "untouchable officials" and "lifetime claim" when no one has suggested that's the case.

If the law is that that an official cannot be fired without cause, then that's that, if there's no cause. Maybe they have a term of employment in that position, and when it ends, they leave. Maybe Congress can fire them via some other appropriate mechanism. But if the law says the president cannot fire them without cause, then that's just not a power the president has.