In a heavy pot with a lid, place the chicken, onion, lemon, salt, pepper, water, bay leaf, and thyme. Simmer over low heat until the chicken is tender, about 1 hour.

Let chicken cool slightly in the pot, then remove and take the meat off the bones. Discard the bones, skin, onion, lemon, and bay leaf. Skim excess fat off the broth if desired. Return broth and chicken pieces to the pot and simmer over low heat.

To make dumplings, in a medium mixing bowl, cut shortening into flour and salt. Add 1/4 cup water (or more if needed) to form a soft dough. Roll dough on a floured surface until very thin. Cut into 1-inch wide strips, then tear 1-inch long pieces.