The night prior to serving, place the pork shoulder skin-side up in an aluminum roasting pan. Score the skin in a criss-cross pattern.
In a mixing bowl, prepare the marinade by adding the minced garlic, naranja agria, sea salt, ground black pepper, ground cumin, dried oregano, and lime juice. Stir the mixture until it becomes consistent.
Generously brush the pork shoulder with the marinade. If desired, store the excess marinade in the refrigerator for sauteing the onions later. Let the pork shoulder marinate in the refrigerator overnight.
Prepare the grill by splitting the coals in half to the left and right side of the grill. Be sure to have the coals lowered as far away from the grill grates as possible. Set the grill temperature to 325 degrees Fahrenheit. If you use a gas grill, only light the rightmost and leftmost burners.
Remove the marinated pork from the roasting pan, and place the pork shoulder on the center of the grill, skin-side up. Pour the remaining marinade from the roasting pan over the top of the pork shoulder.
Continue grilling for at least 3 hours (or 20 minutes per pound), or until the meat temperature closest to the bone reaches 160 degrees Fahrenheit.
Remove the pork shoulder from the grill, and let rest for 30 minutes, or 3 minutes per pound. While the pork shoulder rests, saute the sliced onions on a skillet with the excess marinade from the night before.
Serve the pork shoulder and onions, enjoy!
Naranja agria (sour orange juice) can be found in bottles in the Hispanic section of most major grocery store chains. Bonus points if you can actual sour oranges to juice, as they are very seasonal and difficult to find.