Light one chimney full of charcoal. When all charcoal is lit and covered with gray ash, pour out and spread the coals evenly over entire surface of coal grate. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate. Place sugar in a medium-sized disposable aluminum pan. Dip each of the lemons, cut side down, into sugar. Place lemons on grill, cut side down, and cook until browned, about 5 minutes. Remove from grill.
Add 2 cups of water, honey, and rosemary to pan with sugar. Place pan on grill and whisk until sugar is completely dissolved. Remove from grill and discard rosemary sprigs.
Squeeze lemons into a large large bowl. Pour in honey and sugar syrup and 3 additional cups of cold water and stir to combine. Add additional water or sugar to taste. Transfer to large pitcher, pouring through a fine mesh strainer for a smoother lemonade, if desired. Add in ice to cool, then serve.