Pour olive oil in a large saucepan or Dutch oven over medium heat.
Sauté onions in olive oil until soft, but don't brown them.
Add chicken stock and water to the onions, bring to a boil.
Add rice to the liquids and cook for about 20 minutes, until rice is fully cooked. You will see that the grains have expanded in size.
In a large heatproof mixing cup, crack eggs, whisk them well. Add a cup of hot broth into the egg mixture and quickly whisk it to combine the ingredients.
Pour the eggs and broth mixture into the saucepan with the soup.
Add diced chicken and lemon juice to the saucepan. Stir to incorporate all ingredients.
Bring the soup to a boil and turn the power off.
Serve the soup asap with freshly cut green herbs and ground pepper. Delicious!