Bring a pot of lightly salted water to a boil. Add leeks; cook until tender, about 5 minutes. Drain; transfer to a plate to cool. Chop leeks finely with a sharp knife, or in a food processor.
Combine leeks, ground beef, bread crumbs, and eggs in a large bowl; season with salt and pepper. Mix until combined; shape with hands into walnut-sized meatballs.
Heat olive oil in a large skillet over medium heat. Cook meatballs, turning as needed, until evenly browned, 5 to 10 minutes. Add water, lemon juice, and butter; bring to a boil. Simmer, covered, until meatballs are no longer pink in the center, 15 to 20 minutes.