In a large pot, combine 6 cups of chicken broth, 1/4 cup of fresh lemon juice, 1 cup of shredded carrots, 1 finely chopped onion, and 1/2 cup of finely chopped celery. Stir in 1 tablespoon of chicken soup base and 1/2 teaspoon of ground white pepper. Bring the mixture to a boil over medium-high heat, then reduce the heat and let it simmer for 15-20 minutes, until the vegetables are tender and fragrant.

In a separate bowl, mix together 2 tablespoons of margarine and 2 tablespoons of all-purpose flour to form a smooth paste. Gradually stir this mixture into the simmering soup using a whisk to prevent clumps. Cook for an additional 8-10 minutes, stirring occasionally, until the soup thickens slightly and coats the back of a spoon.

In a clean bowl, beat 3 egg yolks until pale and light. Slowly add a ladleful of the hot soup to the yolks while continuously whisking to prevent curdling. Gradually pour the egg mixture back into the pot, stirring constantly to incorporate it smoothly.

Add 1 cup of cooked white rice and 2 cups of diced cooked chicken to the pot, stirring gently to combine. Heat over low for about 5 minutes, or until the chicken is warmed through and the rice has absorbed the flavorful broth.

Ladle the steaming Greek Lemon Chicken Soup into bowls, ensuring each serving has a good mix of chicken, rice, and tender vegetables. Garnish with fresh lemon slices on top.