Make the seasoning. In a blender, combine the orange juice, ancho chile, garlic, oregano, black pepper, cumin, vinegar and 1½ teaspoons salt. Blend until smooth.
Cook the pork. Using a pressure cooker (like an Instant Pot): Pour the seasoning mixture through a medium-mesh strainer into the cooker, stir in the pork, lock the lid in place and cook on high for 30 minutes; let pressure naturally subside for 15 minutes, then release. In a slow cooker: Spread the pork pieces over the bottom of a 6-quart slow cooker, then pour the chile mixture through a medium-mesh sieve over the meat; cover and cook on high for 4 hours, until the meat is fall-apart tender. On the stove top: Strain the seasoning through a medium-mesh sieve into a 4-quart saucepan, add ½ cup water, stir in the pork, partially cover and cook over medium to medium-low (there should just be a gentle simmer) until the meat is completely tender, about 1½ hours; add more water if the meat starts peeking out. Let cool in the liquid if time allows.
Finish the chilorio. Remove meat from the liquid. Use a fork or fingers to break the pork into coarse shreds. In a very large (12-inch) skillet over medium-high, heat the lard or oil. When hot, add the pork in a single layer. Cook until the meat is brown, stirring occasionally, 3 or 4 minutes. Add ½ cup of the cooking liquid (you may want to spoon off excess fat that has risen to the top) and cook, stirring regularly, until reduced nearly to a glaze. Taste and season with salt, usually about a generous ½ teaspoon. Serve with warm tortillas, salsa and the onion-cilantro mixture.
Note: if you end up with more than ½ cup of braising liquid, boil it over high heat until reduced to ½ cup.