Mix together harissa, thyme, lemon zest and juice, and vinegar for marinade.
Mix salt, paprika, and pepper for dry rub. Stir 1 tablespoon dry rub into marinade. Place pork, skin side down, in a large roasting pan; pour marinade over pork. Flip pork; with a sharp knife, score skin (but not meat) in a diamond pattern at 1/2-inch intervals. Pat remaining dry rub over skin. Cover, and refrigerate at least 8 hours and up to 1 day. Bring to room temperature before roasting, 1 to 2 hours.
Preheat oven to 325 degrees. Cover pan with parchment-lined foil, and roast pork until fork-tender, about 5 hours. Remove foil from pan, and roast 30 minutes more. Raise temperature to 425 degrees, and roast until skin is deep brown and crisp, about 45 minutes. Remove from oven, and tent with foil. Let rest 45 minutes before carving. Serve with harissa-spice barbecue sauce.