Place lemon juice in a small bowl; add oil in a slow, steady stream, whisking constantly. Coat outside skin and inside cavities of chickens evenly with lemon juice mixture; sprinkle evenly with Paul's Chicken Rub, and rub into chickens. Wrap each chicken tightly with plastic wrap, and chill at least 6 hours.
Soak wood chunks in water for at least 30 minutes.
Prepare smoker according to manufacturer's directions, substituting beer for water in water pan. Bring internal temperature to 225° to 250°, and maintain temperature for 15 to 20 minutes.
Drain hickory wood chunks, and place on coals. Place chickens, breast sides up, on upper cooking grate, and cover with smoker lid.
Smoke chickens, maintaining the temperature inside smoker between 225° and 250°, for 2 hours. Remove lid, baste with half of Paul's Barbecue Sauce, and, if necessary, add more beer to water pan. Cover with smoker lid; smoke 1 to 1 1/2 more hours or until a meat thermometer inserted into thighs registers 180°. Serve with remaining half of Paul's Barbecue Sauce.