Combine the first 5 ingredients in a large Dutch oven or stockpot; bring to a boil. Partially cover, reduce heat, and simmer 45 minutes. Remove from heat, and set aside.
Combine the lamb and next 7 ingredients (lamb through garlic) in a bowl, and stir well. Shape the mixture into 24 (1 1/4-inch) meatballs. Place a large nonstick skillet over medium-high heat until hot. Add meatballs, and cook 10 minutes or until browned, stirring frequently. Remove from skillet, and pat dry with paper towels; set aside, and keep warm.
Strain stock through a colander into a large bowl; discard solids. Reserve 2 cups stock; set aside. Return remaining stock to pan, and bring to a boil; add meatballs, rice, lemon juice, beans, and artichokes. Return to a boil, and reduce heat to low.
Place eggs in a bowl; stir well. Gradually add reserved 2 cups stock, stirring constantly with a wire whisk. Slowly drizzle egg mixture into soup, stirring constantly.
Note: Reheat the soup over medium-low heat (do not boil) so the egg does not curdle.