Combine chicken broth, lemon juice, shredded carrots, onion, celery, chicken soup base, and white pepper in a large pot. Bring to a boil over high heat, then lower to a simmer and cook until the vegetables soften, about 15 to 20 minutes.
Whisk margarine and flour together in a small bowl until creamy. Slowly stir this mixture into the simmering soup and keep stirring often while cooking for 8 to 10 minutes until the soup thickens slightly.
In a separate bowl, beat the egg yolks until light and creamy. Gradually add a scoop of hot soup to the eggs while whisking to warm them without curdling. Then pour this egg mixture back into the pot, stirring continuously, and gently heat it through without letting it boil.
Stir in the cooked rice and diced chicken to the soup. Allow everything to heat together for a few minutes.
Serve the soup by ladling it into bowls and topping each with a lemon slice. Enjoy this cozy and tangy delight!