Place ½ cup of the lemon pepper in a gallon-size resealable plastic bag or bowl. Do not add salt. Add 1 quart cold water and stir to mix. Rinse chicken and add to brine. Refrigerate for 2 hours or for up to 8 hours.
Preheat smoker to 225°F.
Remove chicken and pour out brine solution. Sprinkle remaining 2 teaspoons of lemon pepper over the chicken.
Place chicken on middle rack of smoker, breast side up, and smoke for 4 hours (do not open the smoker during cooking) or until internal temperature reaches 165°F.