The Lottery is a representation of something being passed down from generation to generation without someone to question it. Even though bits and pieces of the lottery have changed the people have the same mindset and are fully loyal to their annual sacrifice.
The Box is a main part of the lottery because its not the original box, but the people still believe that there are pieces of the old box in this new one. Showing that people still hold onto the bits and pieces of tradition because that's all they know.
The Stone Pile
The stone is symbolic of the people building up on old traditions, not wanting to be the cause of the stone piles fall just to add onto it. So when the still have insane traditions nobody wants to be the one to say no to it in fear of being stoned themselves.