In a large pot, bring the water or stock to a boil. Add the rice and cook for 10 minutes.
While the rice is cooking, combine the ground beef, ground pork, grated onion, egg, salt, and pepper in a bowl. Mix well and form into small meatballs.
Gently add the meatballs to the boiling broth. Cook for 15-20 minutes, or until the meatballs are cooked through.
In a separate bowl, whisk together the eggs, lemon juice, salt, and pepper. Slowly drizzle a ladleful of the hot broth into the egg mixture, whisking constantly to temper the eggs. Repeat this process a few times.
Slowly pour the tempered egg mixture into the pot with the meatballs, stirring constantly. Cook for 2-3 minutes, or until the soup has thickened slightly. Do not boil.
Serve immediately.