Combine the granulated sugar and water in a small saucepan and place over medium heat. Stir occasionally until the sugar is completely dissolved and the liquid becomes clear, forming a light syrup. Add the lemon zest and remove the pan from heat. Cover and allow the mixture to steep for 1 hour so the citrus oils fully infuse the syrup. Once steeped, strain the syrup through a fine-mesh sieve to remove the zest. The remaining syrup can be stored in the refrigerator for up to one week.

In a high-powered blender, combine ½ cup of the prepared lemon syrup, freshly squeezed lemon juice, coconut milk, and ice. Blend on high until the ice is finely crushed and the mixture takes on a smooth, frosty texture similar to a slush. Pour the whipped lemonade evenly into four 8-ounce glasses. Serve immediately while icy and refreshing.