Heat oil in a 6-quart pot over medium heat. Add carrots, red bell pepper, 1 red onion, and parsley root; cook and stir until slightly softened, 10 to 15 minutes. Pour in water. Add tomatoes and celery. Simmer until flavors combine, about 30 minutes.
Mix ground beef, 1/2 onion, egg whites, rice, flour, 1 pinch dill, salt, and pepper together in a large bowl. Wet your palms with water and roll spoonfuls of the beef mixture into meatballs.
Drop meatballs carefully into the pot. Cook until no longer pink in the center, 30 to 35 minutes. Stir in lovage, garlic herb seasoning, 1/2 teaspoon dill, and parsley. Remove from heat. Stir in lemon juice.
Mix sour cream and egg yolks together in a small bowl. Stir into the soup. Cover and let stand for 15 minutes.
