Bring a large pot of salted water to a boil. Cook orzo in the boiling water until partially cooked through but not too soft, about 5 minutes; drain and rinse with cold water until cooled completely. Set aside.

Heat olive oil in a large pot over medium heat. Add carrots, celery, and onion, saute until the vegetables begin to soften and the onion becomes translucent, about 5 to 7 minutes. Add garlic; cook and stir until fragrant, about 1 minute more. Season with thyme, oregano, salt, black pepper, and bay leaf; continue cooking another 30 seconds before adding chicken broth into the pot.

Bring the broth to a boil. Partially cover the pot, reduce heat to medium-low, and simmer until the vegetables are just tender, about 10 minutes.

Stir in orzo, lemon juice, and lemon zest into the broth; add chicken. Cook until the chicken and orzo are heated through, about 5 minutes. Ladle soup into bowls and serve.