Toss lemon slices and garlic in sugar. Set aside.
Combine bread crumbs and milk in a large mixing bowl. Add chicken, onion, and black pepper. Use your hands to gently combine all of the ingredients. Form into meatballs that are about 1.5-inches in diameter (these should be fairly small; if the mixture sticks to your hands, wet your hands with a small amount of oil or water).
Heat a large saute pan or skillet over medium heat. Add olive oil. When it begins to shimmer, add meatballs. Let meatballs cook on one side until golden brown, then gently turn meatballs until evenly golden brown on all sides, 6 to 8 minutes total. (Note: If the pan starts to look dry or the meatballs start to stick at any point during cooking, add some extra oil.
Set cooked meatballs aside in a bowl.
Pour lemons and garlic into heated pan. Sauté until garlic is fragrant and lemons are tender, 1 to 2 minutes. (Don’t worry if there are a lot of browned bits starting to stick to the bottom of the pan at this point - they’ll come up as soon as you add the liquid.)
Transfer lemons and garlic to bowl with meatballs.
Add butter to heated pan. When it melts, add shallots and cook until tender, about 2 minutes.
Add flour and oregano and stir until no dry spots remain.
Slowly pour in white wine and stock, scraping up any browned bits on the bottom of the pan.
Bring sauce to a simmer and simmer until slightly thickened, 2 to 4 minutes.
Remove pan from heat and gently stir in capers, lemon-garlic mixture, and meatballs.
Top meatballs with parsley.