Tear bread into bite-size pieces, and place in a small bowl. Add ouzo. Let stand for 10 minutes to soak. Squeeze excess liquid from bread. Transfer bread to a medium bowl. Cook onion in 2 tablespoons oil over medium heat, stirring frequently, until soft, about 6 minutes. Add onion to bowl with bread.
Add ground beef to bowl, and break up with your hands. Stir in egg and yolks, capers, garlic, mint, oregano, and salt. Season with pepper. Knead mixture until well combined, then use a spoon to stir until smooth. With moistened hands, shape mixture into 1-inch meatballs, and place on a tray. Cover, and refrigerate for 1 hour.
Heat remaining 2 tablespoons oil in a heavy skillet over medium-high heat, and cook meatballs in batches, about 12 at a time, turning until evenly browned, about 5 minutes. Add fresh oil as needed for each batch. (While you work, keep cooked meatballs warm on a rimmed baking sheet in a 200-degree oven.) Finely grate lemon over meatballs, and serve warm.