Place the turkey carcass in a large soup pot and cover with water. Some of the carcass may stick out of the top and that's perfectly fine. As it cooks, the bones will eventually break down. Add the chopped onion, carrots, celery, black peppercorns and herbs. Squeeze both halves of the lemon into the soup pot and drop the lemons in the stock.
Place over medium high heat for about 10 minutes. Once the water warms up, turn it to medium-low and let it simmer gently for 4-12 hours. The longer you cook it, the deeper and richer the flavors will be. Stir the stock occasionally, but you can mostly leave it alone, merely adding more hot water if needed.
Once it's ready, strain the bones and veggies from the stock and toss. Reserve the stock to make soup or freeze it. Once you make soup, be sure to taste the stock and add salt, as needed.