Heat the oven to 300 degrees F. Score meat's skin with a sharp knife, making a cross-hatch pattern. Pulse onion, garlic, oregano, cumin, chile, salt, and pepper together in a food processor, adding oil in a drizzle and scraping down sides as necessary, until mixture is pasty. Alternatively, mash ingredients in a mortar and pestle. Blend in the vinegar.
Rub this mixture well into pork, getting it into every nook and cranny. Put pork in a roasting pan and film bottom with water. Roast pork for several hours, a 4-pound shoulder may be done in 3 hours, turning every hour or so and adding more water as necessary, until meat is very tender. Finish roasting with the skin-side up until crisp, raising heat at end of cooking, if necessary.
Let meat rest for 10 to 15 minutes before cutting it up; meat should be so tender that cutting it into uniform slices is almost impossible; rather, whack it up into chunks. Serve with lime.