Toss the carrots and celery together in a slow cooker. Add the dill, thyme, bay leaf, onion and 1/2 teaspoon salt.
Rub the chicken thighs all over, including under the skin, with 1 teaspoon salt total, and place 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 rice. While the rice warms through, remove and discard the chicken skin and bones and shred the chicken (it will mostly fall apart on its own).
After the 15 minutes, turn off the slow cooker and remove the dill and thyme stems and the bay leaf. 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 dill. Serve hot topped with whole dill fronds.
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