Keep playing to unlock new items and improve your reward.
Lottery can be seen in the title screen, Abandoned Train in Arizona, and Gem's Saloon in Oregon. You can also teleport to the lottery when you touch the red "LOTTERY" button (appears when you are focused Swarm Gun, Submachine Gun or any other lottery item at the shop). The same button is also in the pause menu. Common items in each individual lottery include a certain quantity and quality of medicine, outfits, elixirs, Sheriff Stars, and even coins. The higher the lottery, the higher the reward.
Gold Bullet Chest - Gold Bullet Chest costs 20 Sheriff Stars and gives you a chance to get Swarm Gun, Light Cannon, Machinist set, Mayhem Gauntlet, and much more premium items not newly introduced in a recent update. Sheriff stars unfortunately do not show up as a prize.