Preheat grill for medium heat and lightly oil the grate.
Pour sugar into a saucepan; press halved lemons and limes cut-side down into the sugar.
Set the saucepan with remaining sugar on grill; stir in 2 cups of water and whisk over the heat until dissolved into a syrup. Let cool.
Place lemon and lime halves sugared-side down on grill and cook until browned, about 5 minutes.
Place lemon and lime slices on the grill; cook until browned, 30 to 60 seconds on each side.
Juice halved lemons and limes into a large pitcher. Add syrup and 2 cups water to the juice, 1/2 cup at a time, until the limeade achieves desired sweetness. Pour limeade into glasses filled with ice; garnish each glass with a grilled citrus slice.