Sauté the celery, carrots, and onions in a large soup pot with the butter and oil over medium-high heat for 5-7 minutes.
Stir in the garlic and cook for about 30 seconds, then add the flour and cook for another minute or so.
Use a small amount of broth to deglaze the stockpot
Pour in the rest of the broth and stir until the flour has dissolved. Bring the soup to a boil. If using uncooked chicken breasts, add them now.
Cover the soup (lid slightly open), season, and reduce the heat and simmer for 15 minutes.
Stir in the orzo and cook for another 10 minutes or until the orzo is cooked through. If using pre-cooked chicken, add now. Remove lid and stir often to prevent orzo from sticking.
If using uncooked chicken breasts, take the chicken out of the pot and cut it up, then add it back in.
Squeeze the lemon into the soup and season to taste. Serve immediately.