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.
Actually, if it doubles every time and we assume 8 billion is the max, you only need 32 people to not pull it. Maybe I'd bet on that. If I was in the middle I'd let it pass no question.
What if no one ever pulls it?
Assuming the problem is infinite and considers physical factors, then it would happen at one point
Eventually it could come to a Joker guy who wants to kill as many people as possible, and you've given them the opportunity.
Maybe eventually you're just killing lilliputians and borrowers, so... Win win.