In a large pot or Dutch oven, heat oil over medium-high. Once hot, add carrots, celery, onion, garlic, thyme and bay leaves, and season with salt and pepper. Sauté vegetables until they begin to soften and slightly brown, about 4-5 minutes. Add chicken stock, chicken, lemon zest and juice, dill and parsley, and bring to a rolling boil. Reduce heat and simmer for 10-15 minutes. Discard bay leaves.
To serve, portion 1 cup of zoodles in bowls and pour hot soup over them.*