The short answer is no. Simon does not pull a lever to kill Piggy; in fact by the time Piggy comes to castle rock, Simon is long dead. It is Roger, the true sadist of the group, who pulls the lever to drop the giant rock on Piggy.
In fact, Roger is one of the most fascinating characters in the book as he finds his way to being a true sociopath slowly as the story progresses. At first he plays games like throwing rocks at one of the littluns but not actually hitting him; the taboo is still strong.
The taboo against violence is slowly worn away and Roger first demonstrates it by ramming his spear into the pig's rear end and laughing at the pain and torture. The final demonstration comes when he calmly and purposefully kills Piggy with the giant rock.
Simon is nearly the opposite of Roger as he is arguably the most caring boy among the group. He watches out for the littluns and is the only one who sees that the beast is their fear, the darkness and capacity for violence that exists inside all of them.