In small bowl, whisk together 1/4 cup lemon juice, 4 T mustard and black pepper. Place chicken in large zip-lock bag. Pour marinade over chicken and zip the bag close. Massage the chicken in the bag to ensure all pieces are covered with the marinade. Place bag in refrigerator.
Chill at least 2 hours and up to 4 hours, turning occasionally.
Melt butter in heavy small saucepan over medium heat. Add rosemary, garlic and remaining 1/4 cup lemon juice and 2 T mustard. Simmer basting sauce 5 minutes, whisking occasionally. (Can be made 4 hours ahead. Let stand at room temperature.).
Prepare barbecue (medium heat). Rewarm basting sauce. Place chicken on rack. Cover barbecue and grill 2 minutes. Uncover and grill until cooked through, basting occasionally with sauce from pan, about 5 minutes per side.