Bring the water to a boil in a large pot. Add the chicken, 1 teaspoon salt, onion, celery, garlic, bay leaf and parsley to the pot. Reduce heat to simmer and cook the chicken, uncovered, for 2 hours. The liquid will reduce by about one third.
When the chicken has cooked, remove it from the pot and set it aside. Strain the stock to remove all the vegetables and floating scum. You only want the stock and the chicken, so toss everything else out.
Pour 1 1/2 quarts (6 cups) of the stock back into the pot (keep the leftover stock, if any, for another recipe--it can be frozen). You may also want to use a smaller pot or a large saucepan for this. Add coarsely ground pepper, the remaining 1/2 teaspoon salt and the lemon juice, then reheat the stock over medium heat while preparing the dumplings.
For dumplings, combine flour, baking powder, salt and milk in a medium bowl. Stir well until smooth, then let the dough rest for 5 to 10 minutes. Roll the dough out onto a floured surface to about a 1/2-inch thickness.
Cut the dough into 1/2-inch squares and drop each square into the simmering stock. Use all of the dough. The dumplings will first swell and then slowly shrink as they partially dissolve to thicken the stock into a white gravy. Simmer 20 to 30 minutes until thick. Stir often.
While the stock is thickening, the chicken will have become cool enough to handle. Tear all the meat from the bones and remove the skin. Cut the chicken meat into bite-size or a little bigger than bite-size pieces and drop them into the pot. Discard the skin and bones. Continue to simmer the chicken and dumplings for another 5 to 10 minutes, but don't stir too vigorously or the chicken will shred and fall apart. You want big chunks of chicken in the end.
When the gravy has reached the desired consistency, ladle four portions into bowls and serve hot.