In the bowl of a slow cooker combine the raw chicken, carrots, onion, celery, garlic, olive oil, chicken broth, water, thyme, rosemary, bay leaves, and salt and pepper to taste. Cover and cook on low until the chicken is cooked through, about 6 hours. Or cook on high for about 3 1/2 hours.
Remove the cooked chicken to a cutting board an let rest for 10 minutes. Cut into bite-sized chunks. Add the egg noodles and parsley to the slow cooker, increase temperature to high, cover and cook for 10 minutes or until the noodles are tender. Stir in the lemon juice and return the chicken to the slow cooker. Taste and adjust seasonings if necessary.
Serve hot with saltine crackers, if desired.