Preheat smoker using a mix of hickory and a few oak wood chips. The fire should burn down to the coals, not ash, when cooking the pork shoulder.
Season the pork shoulder with a little salt and place the meat on the grill. Cover the smoker and let the pork smoke for 8 to 10 hours.
Combine the rest of the ingredients in a saucepan and bring to a boil. Reduce to a simmer, stirring the sauce frequently. If you like your sauces a little spicier, add more black pepper. After about 20 minutes, remove the saucepan from the heat and set aside.
Once the pork is finished cooking, remove from the smoker and let rest for 5 to 10 minutes. Then, hand pull, chop, or slice the pork. Serve the meat with some of the Lexington dipping sauce poured over the top.