In a large pot, combine the chicken broth, freshly squeezed lemon juice, shredded carrot, finely diced onion, minced celery, chicken soup base, and ground white pepper. Bring the mixture to a boil over high heat, then reduce the heat and let it simmer for 15–20 minutes, or until the vegetables are tender. This helps develop the aromatics and bright flavor of the soup base.
In a small bowl, mix the margarine and all-purpose flour together until a smooth paste forms. Gradually stir this mixture into the simmering soup base from Step 1. Continue cooking and stirring frequently for 8–10 minutes, until the soup thickens slightly. I like to make sure the roux is well blended to avoid any lumps in the soup.
Beat the egg yolks in a separate bowl until they are pale and creamy. Slowly ladle a small amount of the hot soup into the yolks, whisking constantly to prevent curdling. Gradually pour the tempered egg mixture back into the pot with the soup, stirring continuously. Gently heat the soup through without allowing it to boil, to create a silky texture.
Add the cooked white rice and diced cooked chicken to the soup. Cook for a few minutes more, just until everything is heated through. For an extra fresh burst of flavor, I sometimes add an extra squeeze of lemon juice at this stage, but that’s optional.
Ladle the finished soup into serving bowls. Garnish each portion with a slice of lemon and serve immediately. Enjoy the tangy, comforting flavors of this lemon chicken soup.