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Heat a stockpot over medium-high heat. Pat chicken dry with paper towels; sprinkle with salt and pepper. Add oil to the pot and cook chicken in batches, skin-side down, until golden brown, 3 to 5 minutes. Remove chicken from the pan. Discard skin and drippings, reserving 2 tablespoons in the stockpot. Cook and stir onion in the drippings over medium-high heat until tender, 4 to 5 minutes. Add garlic; cook for 1 minute longer. Pour in broth and stir to loosen browned bits from the pan. Bring to a boil. Return chicken to the pot and add celery, carrots, sweet potatoes, bay leaves, and thyme. Reduce heat to low, cover, and let simmer for 10 minutes. Add kale and mushrooms; continue to simmer until chicken is tender and no longer pink in the centers, 15 to 20 minutes. Transfer chicken to a plate. Remove soup from heat and add noodles. Let stand, covered, until noodles are tender, 20 to 22 minutes. Meanwhile, when chicken is cool enough to handle, remove meat from bones and shred into bite-size pieces. When noodles are tender, return chicken to the stockpot. Stir in lemon juice. Season with salt and pepper to taste. Remove bay leaves and serve.