Combine lemon slices with garlic and sugar. Set aside. (Reserve the other half of the lemon to squeeze over the finished dish.)
Combine bread crumbs and milk in a large mixing bowl. Add all of the remaining ingredients for the meatballs. 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, rub a small amount of oil between your hands).
Heat a large saute pan or skillet over medium heat. Add olive oil. When it begins to shimmer, add the meatballs. Let the 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 a splash of water.)
Transfer the cooked meatballs to a plate near the stove.
To the heated pan, add the butter. When the butter melts, add shallots and the lemon slices. Cook, stirring frequently, until the garlic is fragrant and the lemon slices and shallots are tender, 2 to 3 minutes.
Add the flour and oregano and stir until no dry spots remain.
Slowly pour in the white wine and stock, scraping up any browned bits on the bottom of the pan.
Bring the sauce to a simmer and simmer until thickened, 2 to 4 minutes.
Remove the pan from heat and stir in the capers and then the meatballs, spooning the sauce over top.
Squeeze the juice from the reserved lemon half over top. Top the meatballs with parsley.