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.
Add the flour and cook for another minute or so.
Pour in the chicken broth and stir until the flour has dissolved.
Add the Italian seasoning and chicken. Bring the soup to a boil.
Cover the soup with the lid slightly open, reduce the heat, and simmer for 15 minutes.
Stir in the orzo and cook for another 10 minutes or until cooked through. Keep the lid off and stir fairly often to prevent sticking.
Remove the chicken from the pot and cut it up, then add it back in.
Add the lemon juice, parsley, and season with salt and pepper as needed.
Serve immediately.