Over low heat, warm the corn oil in a large heavy pot (preferably one that can be carried to the table). Add the onions and stir to coat them with oil. Cover and cook them slowly for 20 minutes.
Uncover the pot and raise the heat to moderate. Stir in the garlic and serrano chile and saute for 2 minutes. Then add the tomato and continue to cook, stirring for 1 more minute.
Add the stock, lime juice and zest and salt and pepper. Bring the soup to a boil. Lower the heat and simmer, uncovered, for 30 minutes.
Meanwhile, prepare the Blue Corn Dumplings. Sift the corn flour, baking powder and salt into a medium-sized bowl. Using your fingers, two knives, or a pastry cutter, cut in the vegetable shortening until the mixture resembles fine crumbs.
In a small bowl, beat together the egg and milk. Add the cilantro. Gradually stir the egg mixture into the corn flour mixture, adding only enough of the egg to moisten the flour thoroughly. The dough should not be too wet. Depending on the size of the egg, you may not need to use it all.
When the soup has cooked for 30 minutes, drop the dough into the simmering broth a tablespoon at a time to make a dozen dumplings. Cover the pot with a tight-fitting lid, and steam the dumplings for 15 minutes. Keep the soup at a low bubble, and do not lift the lid while the dumplings are cooking.
Bring the cooking pot to the table and serve the soup hot in Mexican-style bowls, with two dumplings floating in each.