Step 1

In a small saucepan over medium heat, bring the sugar and the water to a simmer and cook, stirring occasionally, until the sugar dissolves.

Step 2

Stir the lemon zest into the simple syrup and transfer the saucepan from the heat.

Step 3

Cover the saucepan and let the lemon simple syrup steep for 1 hour.

Step 4

Strain the lemon simple syrup through a fine-mesh sieve and discard the zest. There will be extra lemon simple syrup, which can be refrigerated for up to 1 week.

Step 5

Add 1/2 cup of the lemon simple syrup, the lemon juice, the coconut milk, and the ice to a blender and blend until the ice is crushed and the mixture is slushy.

Step 6

Divide the frozen lemonade between four 8-ounce glasses and garnish with the lemon slices.

Step 7

Serve immediately.