Melt the butter in a large saucepan over medium heat. Add the onion, carrots and celery. Cook, stirring occasionally, until tender, about 4 minutes. Stir in garlic until fragrant, about 1 minute.
Add chicken broth, bay leaves, thyme, salt, pepper and chicken. Bring to a boil, reduce heat and simmer, covered, until chicken is cooked through, about 35 minutes.
Remove the chicken. Once chicken has cooled, remove the meat from the bones, discard the bones. Cut the meat into small pieces.
Stir in chicken and egg noodles. Cook noodles according to package instructions.
Remove from heat, stir in parsley and lemon juice. Discard bay leaves before serving.