Preheat grill to medium heat (275°F to 325°F).
To create a rub, finely chop the salt, rosemary, and lemon zest, and mix. Add pepper.
Rinse and dry the chicken. Carefully loosen the skin of the chicken using a knife, or your hands, to evenly distribute the rub under the skin of the chicken. Brush the chicken with the olive oil. Halve the lemon and squeeze both halves over the chicken.
Open the can of lemonade and pour out ¼ cup, leaving the rest in the can. Place the lemonade can inside the chicken cavity and place the chicken upright on the grill. Grill for 30 minutes, then carefully remove the can and turn the chicken over. Grill for an additional 35 minutes or until the internal temperature reaches 165°F.
Remove chicken from grill, wrap in aluminum foil, and let it rest for 10 minutes. Carve and serve.