Prepare the broth and vegetables. Place the chicken broth, fresh lemon juice, shredded carrot, diced onion, minced celery, chicken soup base, and ground white pepper in a large pot. Bring the contents to a boil over high heat, then lower the heat and simmer for 15–20 minutes, or until the vegetables become tender.

Thicken the soup. Blend the margarine with the all-purpose flour in a small bowl until a uniform, smooth paste is formed. Gradually stir this mixture into the simmering soup, mixing thoroughly so that no lumps remain. Continue cooking for 8–10 minutes, stirring frequently, until the broth develops a slightly thicker consistency.

Temper the egg yolks. In a separate bowl, whisk the egg yolks until pale and creamy. While whisking continuously, slowly add a small quantity of the hot thickened soup to the yolks. Gradually return the tempered yolk mixture to the pot, stirring constantly as it is incorporated.

Heat gently. Continue warming the soup over gentle heat without allowing it to return to a boil. This careful heating helps preserve the smooth, silky texture of the egg-enriched broth.

Add the chicken and rice. Stir the cooked white rice and diced cooked chicken into the soup. Cook for a few additional minutes, only until both ingredients are thoroughly heated.

Serve. Portion the hot soup into individual bowls and garnish each serving with a lemon slice. Serve immediately.