Toss the carrots and celery together in the slow cooker. Add the onion, sprigs parsley, thyme, bay leaf and 1 teaspoon salt.
Rub the chicken thighs all over, including under the skin, with 1 teaspoon salt total, and put them on top of the vegetables. Add the chicken broth. Cover, and cook on low for 8 hours. During the last 15 minutes of cooking, remove the chicken and stir in the noodles.
While the noodles cook, remove and discard the chicken skin and bones and shred the chicken-it will mostly fall apart on its own. When the noodles are done, turn off the cooker, remove the parsley and thyme stems, and add the shredded chicken and 1 tablespoon lemon juice. Taste, and add more lemon juice and salt as needed. Stir in a good amount of pepper and the chopped parsley, and serve hot.
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