Psarosoupa - Fish Soup

Clean the fish and leave only the fillet. Season with salt and pepper. Cut into small pieces. Clean and cut the carrot, celery and onion into pieces. Put the water in a pan, add the onion, carrot and celery. Bring to high heat and wait to boil. Lower the heat and cook for about 30 minutes. Remove the pan from the heat and pass through a sieve. Return the broth to the pan and discard the vegetables. Bring the stock to a low heat. Add the fish pieces in the broth and cook for 10 minutes. Remove the fish pieces with a slotted spoon and place on a plate. Add the rice to the broth and cook for about 20 minutes or until soft. Place the egg in a container and beat with a fork. Add a little broth to the egg mixture, and continue beating. Add about 1 cup of broth to the egg, little by little. Now, return the egg to the broth of the pan and mix well. Add the lemon juice and let the soup heat up but do not let it boil. Remove the soup from the heat and serve. Apart, serve the accompanying fish.