In a large pot, combine 6 cups of chicken broth, 1 cup of fresh lemon juice, 1 cup of shredded carrots, 1 finely chopped onion, and 1 chopped celery stick. Add 2 tablespoons of chicken soup base and 1 teaspoon of ground white pepper. Bring the mixture to a boil over medium-high heat, then reduce to a simmer and cook for 15-20 minutes, until the vegetables are tender and fragrant.

In a small bowl, mix 2 tablespoons of margarine with 2 tablespoons of all-purpose flour to form a smooth paste. Gradually stir this paste into the simmering soup, ensuring no lumps form. Continue cooking for an additional 8-10 minutes while stirring occasionally, until the soup thickens.

In a separate bowl, beat 2 egg yolks until light and creamy. Carefully whisk in a ladle of the hot soup to gently warm the yolks without cooking them, then slowly add the tempered egg yolk mixture back into the pot while stirring vigorously.

Gently fold in 1 cup of cooked rice and 2 cups of diced cooked chicken into the pot. Heat the mixture on low, stirring occasionally, for about 5 minutes.

Ladle the soup into bowls, garnishing each with lemon slices. Serve immediately while warm.