In a bowl, beat 1 egg to blend. Add rice, beef, onion, lemon peel, lemon juice, oregano, 1/4 teaspoon salt, and 1/8 teaspoon pepper; mix well.
Put flour on a rimmed plate. Shape meat mixture into 1-inch balls, rolling each in flour as formed; shake off excess. Set balls slightly apart on a sheet of waxed paper.
In a 5- to 6-quart pan over high heat, bring broth to a boil. Add meatballs, reduce heat, and simmer just until no longer pink in the center (cut to test), about 15 minutes.
Add spinach leaves and stir gently until wilted, about 5 minutes. In a small bowl, beat with a fork remaining egg to blend. Pour into soup, stirring. Ladle soup into wide bowls. Add salt and pepper to taste.