Heat the lard or vegetable oil in a large casserole set over medium-high heat. Add the pork pieces, sprinkle with salt and pepper, and let the meat cook for a minute or two. Add the onion, stir and let cook for a minute or two. Incorporate the diced tomatoes, mix well, cover and reduce heat to medium low.
Cook, stirring occasionally, until the meat is completely cooked through and the tomatoes have cooked down into a mushy paste, about an hour to an hour and 10 minutes. Remove the lid, taste for salt and add more if need be, stir, and continue cooking until there is almost no moisture in the casserole.
To serve, place two toasted corn tortillas on a plate, spoon refried black beans on top and ladle the meat on top of the beans. Place a couple avocado slices on the side.