Trim excess fat from the lamb shoulder, leaving about a quarter-inch of fat. Rinse under cold water and pat dry with paper towels.
Prepare dry rub seasoning by combining all ingredients in a small bowl. Use a fork to remove or crush any small clumps that appear.
Apply dry rub seasoning to lamb shoulder. Apply generously all over, working it into any small crevices or folds in the meat. Leave lamb shoulder to sit at room temperature for 30 minutes.
While lamb shoulder sits, fire up smoker to 250°F (121°C). If you are using a charcoal grill, ensure it’s set up for 2-zone cooking. Add smoking wood chips to coals or your smoker’s wood chip tray.
Place lamb shoulder on smoker grates, or on your grill’s grates in the indirect cooking zone (away from direct heat). Place lamb shoulder fat side up and bone side down.
Close smoker lid or door and smoke for 5 hours, or until lamb internal temperature reaches 165°F (74°C). After the first 2 hours, spritz the shoulder every 30-60 minutes with apple juice filled into a spray bottle.
Once the meat has reached 165°F, wrap the shoulder in aluminum foil and apple juice. Place back in the smoker and increase the temperature to 300°F (150°C). Smoke until internal temperature hits 195°F-205°F (90-96°C).
Remove the lamb shoulder from the smoker and tent in aluminum foil. Rest for 30 minutes.
Pull or slice the meat to serve.