I think you would HAVE to pull it right? Regardless of how many times the lever can be given to the next person, you are either killing 1/3rd lives in the scenario, or you are killing 1/8bil.
What if no one ever pulls it?
Assuming the problem is infinite, then it would happen at one point
Actually, if it doubles every time and we assume 8 billion is the max, you only need 33 people to not pull it.