Fill a large soup pot three-quarters full with water and bring to a boil.
Meanwhile, in a large bowl, combine beef, onion, rice, parsley, dill, olive oil, cumin, mayonnaise, carrot, salt and pepper. Form into small meatballs and coat each meatball in flour. Ease the meatballs into the boiling water, cover and reduce heat to low. Simmer, stirring occasionally, until meatballs are no longer pink and soup has thickened slightly, 15 minutes.
In a small bowl, beat eggs with lemon juice. Stir a spoonful of hot soup into egg mixture and beat well. Then pour egg mixture into soup and stir. Serve hot.
