Pat the chicken dry with paper towels and sprinkle with salt and pepper on both sides. In a large Dutch oven, heat the oil over MEDIUM-HIGH heat. Add the chicken and cook until dark golden brown, about 3 to 4 minutes on each side. Remove chicken from the pan and discard all but about 2 tablespoons drippings (if there's not enough drippings, add a touch of neutral oil).
Add the onion and celery to the drippings and saute over MEDIUM-HIGH heat until tender, 3 to 4 minutes. Add the garlic and sage and cook 1 minute longer. Add the stock, stirring to loosen the browned bits from the pot. Increase the heat to bring the liquid to a boil then return the chicken to pot. Add the carrots, bay leaves and thyme sprigs (or minced thyme leaves). Reduce the heat to LOW, cover, and simmer until the chicken is tender, 25 to 30 minutes.
Remove the the pot from the heat and transfer the chicken to a cutting board. Remove and discard the woody stems of the thyme sprigs (most of the leaves will be left behind in the broth).
Bring the liquid back to a gentle simmer and add the uncooked noodles. Simmer uncovered for 5 to 6 minutes, stirring occasionally.The noodles should be tender but still have a little bite. Cooking time will vary depending on the type of egg noodles used. Cook for the amount of time as directed on the package for the best results.
Meanwhile, using 2 forks, remove the meat from the bones. Shred the meat with the forks then run a knife through it to cut into smaller, bite-size pieces, if needed. Discard the skin and bones
Remove the pot from the heat and add the shredded chicken. Stir in the parsley and lemon juice. If desired, adjust seasoning with additional salt and pepper. Remove and discard bay leaves and serve.