In a large saucepan, combine the chicken broth, bouillon, rice, carrots, celery and onion. Bring to a boil. Reduce heat; cover and simmer for 20 minutes, or until rice and vegetables are tender. Stir in the chicken. Remove from heat and set aside.
In a small saucepan, melt the butter over medium heat. Whisk in the flour. Cook 1 minute, whisking constantly, until smooth and bubbly. Gradually whisk in 2 cups of the broth; cook until slightly thickened, whisking constantly. Remove from heat and set aside.
In a small bowl, beat the eggs until frothy. Gradually beat in lemon juice and 2 cups of the thickened broth mixture. Slowly add the egg mixture to the rest of the broth mixture in the large saucepan, stirring constantly. Heat gently until the soup thickens enough to coat a spoon, stirring frequently (do not boil). Add salt and pepper to taste.
Ladle into soup bowls and garnish each with a lemon slice and a sprinkle of green onions.
Notes
If you are preparing this recipe as GLUTEN FREE, please make sure that you are using brands of the following ingredients that are known to be GF: chicken broth and bouillon. Also sub GF flour or an alternative thickener for the all-purpose flour.