Simmer the Base: In a large pot over medium heat, combine the chicken broth, chicken soup base, ground white pepper, carrots, onion, and celery. Let it simmer for about 10 minutes.
Make the Roux: In a separate saucepan, melt the margarine over medium heat. Stir in the flour, cooking until lightly golden. Gradually whisk in 1 cup of the hot broth to create a smooth paste.
Thicken the Soup: Slowly pour the roux mixture back into the main pot, stirring continuously. Let it cook for another 5 minutes until slightly thickened.
Temper the Eggs: In a bowl, whisk the egg yolks. Gradually add 1 cup of the hot soup to the eggs while whisking constantly. Once blended, slowly stir the egg mixture back into the soup.
Add Chicken & Rice: Stir in the cooked rice and diced chicken. Cook for another 5 minutes until heated through.
Finish with Lemon: Pour in the fresh lemon juice and stir well to combine.
Serve & Garnish: Ladle into bowls and top with lemon slices for a refreshing citrus boost. Enjoy warm!