Bring sugar and water to a boil over medium heat, stirring occasionally. As soon as the sugar has dissolved, add the lemon peel. Let the lemon peel boil in the syrup for a few minutes, then remove from the oven and let it steep for an hour. Filter the syrup with a sieve so that only the liquid remains.
Put the syrup, lemon juice, coconut milk and ice cubes together in a blender and mix until the ice is completely crushed. Pour into 4 glasses and serve immediately.