Preheat outdoor smoker to approximately 225 degrees F.
Rinse chicken with cold water and pat dry.
Combine oil, BBQ rub, chipotle powder and lemon pepper in a small bowl. Use a brush to coat the entire chicken in the mixture.
Place chicken in the smoker and smoke until internal temperature of chicken reaches 180 degrees F on an instant-read thermometer, about 3 hours.
Brush with BBQ just before serving, if desired.
In a small saucepan, combine all ingredients and bring to a simmer for flavors to combine.