Maybe you could have a major scandal or fraud associated with the lottery process, causing public outcry and forcing it to stop. Another option could be if the main characters decide to expose the negative aspects and actively campaign against it.
The lottery in the story works in a very primitive and cruel way. Everyone participates, and the one whose name is drawn is chosen as the victim with no clear reason or logic behind it. It seems to be a blindly followed ritual without any real purpose.
To be honest, I can't recall who wins the lottery precisely in that short story. It's a story that keeps you guessing until the end. Maybe you should give it a read and figure it out for yourself.