In a large saucepan, combine chicken broth, bouillon cube, rice, carrots, celery, and onion and bring to a boil. Reduce heat, cover, and simmer for 20 minutes or until rice and vegetables are tender. Stir in chicken and remove from heat.
In a small saucepan, melt butter and stir in flour until smooth. Gradually add 2 cups of broth mixture and cook until slightly thickened, stirring constantly.
In a small bowl, beat eggs until frothy.
Gradually beat lemon juice and 2 cups thickened broth into the large pot of soup. Very slowly add egg mixture into the soup, stirring constantly. Do not do this if the soup is boiling or very hot, otherwise eggs will scramble. If the soup is too hot, remove the pot from heat for a few minutes before adding the eggs. Gently heat soup until it thickens enough to coat a spoon, but do not boil. Season to taste with salt and pepper. Garnish with lemon slices and chopped green onion or parsley, if desired.
Recipe originally inspired by Food.com with 5-star rating and 80 reviews.