Combine 1 thinly sliced lemon and 1 2/3 cups superfine sugar in a bowl; mash with a spoon. Add 3 cups cold water and 1 1/4 cups lemon juice; let stand for 5 minutes, stirring occasionally. Strain. Puree half of lemon juice mixture and 4 cups ice in a blender until smooth. Pour into 4 chilled glasses; repeat. Serves 8.