Common themes include power - up. Since the OC has the lottery to potentially get amazing items or powers, and their gamer knowledge, they usually go through a process of becoming more powerful. Also, adaptation is a theme. They have to adapt their gamer mindset and lottery - influenced abilities to fit into the Naruto world's ninja culture. And of course, there's often a theme of discovery, as they discover new things about the Naruto world and themselves through their experiences.
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.
One popular 'Naruto OC Gamer with Lottery' fanfiction is 'The Gamer's Naruto Adventure'. It has an interesting plot where the OC uses their gamer skills along with lottery - won items to change the Naruto world. Another is 'Lottery Luck in Naruto', which focuses more on how the lottery system affects the OC's relationships in the Naruto universe.