For brine, combine the first seven ingredients in a large kettle. Bring to a boil; cook and stir until salt is dissolved. Remove from the heat. Cool to room temperature. Meanwhile, grate peel from lemons. Juice lemons and reserve juiced lemon halves; set aside.
Remove giblets from chicken; discard. Place cold water in a 2-gal. resealable plastic bag; add chicken. Place in a roasting pan. Carefully pour cooled brine into bag. Squeeze out as much air as possible; seal bag and turn to coat. Refrigerate for 3-4 hours, turning several times.
Discard brine. Rinse chicken with water; pat dry. Rub inside of chicken with 1 teaspoon rosemary and 1/8 teaspoon each salt and pepper. Place the juiced lemon halves in cavity. Skewer chicken openings, tie together.
Place chicken on rotisserie rod on grill with a drip pan according to manufacturer's directions. Combine olive oil, lemon juice, lemon peel, remaining rosemary, salt and pepper; brush over chicken. Grill 1 to 1-1/2 hours or until chicken juices run clear.