In a medium-sized cooking pot, add 3 liters of water, along with the 100 ml of olive oil and bring to a boil.
Season with salt and pepper.
Once the water is boiling, start adding the meatballs one by one. Use a spoon to carefully dip each one.
NOTE: If the temperature of the water drops while you add the meatballs, put the pot's lid back on, and wait for a minute or two until water starts to boil again. This way when you drop the meatball into the boiling water, the meatball gets firm right away and won't break and crumble.
Once you have added all the meatballs and the water is boiling, reduce heat to medium and with the lid back on, simmer for about 30-40 minutes.
Add the rice and celery, and simmer for another 20 minutes or until rice is cooked.
Remove from heat and set aside for 10 minutes for the temperature to drop slightly.
In a small mixing bowl whisk the eggs along with 2 tablespoons of water.
Using a ladle, take a spoonful of the soup and start pouring it into the eggs (tiny drops at a time) while stirring vigorously and constantly. Continue until you add at least half of the soup into the eggs, and then transfer back to the pot.
Stir in the fresh lemon juice and serve!