Heat a large pot over medium heat and add the olive oil.
Add the onion and sauté for 5-7 minutes until softened and translucent.
Add the garlic, celery, and carrot and cook for a few more minutes.
Pour in the chicken and lamb/beef stock. Stir and bring the mixture to a gentle simmer.
Add the orzo to the simmering broth. Cook for 8–10 minutes, stirring occasionally, until tender.
In a medium bowl, whisk the eggs until frothy. Gradually whisk in the juice of 3 lemons.
Slowly ladle 1–2 cups of the hot broth into the egg mixture, whisking constantly to prevent curdling.
Remove the pot from the heat and slowly pour the tempered egg mixture back into the pot, stirring constantly.
Stir in the shredded chicken. Let it heat through for 2–3 minutes before serving. Top with fresh parsley if using.