Warm the stock in a medium-large pot so that it starts to simmer. Add the rice, cover and bring back to a simmer. Reduce the heat and leave the rice to cook (timing will depend on the type of rice - see packet for expected time).
Once the rice is just tender, add the chicken to the pot and stir through.
Whisk together the egg, egg yolk and lemon juice in a small bowl or jug. Add a small spoonful of the warm stock and whisk in, then repeat a couple times. Add the mixture into the pot of soup and stir it through.
Serve the soup, getting a good balance of rice, chicken and the stock in each bowl, and top with a little dill. Season with salt and pepper to taste (and a little more lemon if you like, too).
Video
Notes
Note - you can also use orzo pasta instead of rice.