**Cook the Rice:** In a large pot, bring the chicken broth to a boil. Add the rice and cook until tender, about 15-18 minutes. Reduce the heat to low.
**Add the Chicken:** Stir in the cooked shredded chicken and let it warm through for 2-3 minutes.
**Prepare the Egg Mixture:** In a medium bowl, whisk the eggs until frothy. Gradually whisk in the lemon juice.
**Temper the Eggs:** Slowly ladle a small amount of hot broth into the egg mixture, whisking constantly to prevent curdling. Repeat this process with 2-3 more ladles of broth.
**Incorporate the Egg Mixture:** Pour the tempered egg mixture back into the pot, stirring continuously. Cook on low heat for 1-2 minutes until the soup thickens slightly. Do not let it boil.
**Season and Serve:** Season the soup with salt and pepper to taste. Garnish with fresh parsley or dill if desired, and serve immediately.