In a small saucepan, combine 1/2 cup of water and the granulated sugar. Heat over medium heat, stirring occasionally, until the sugar has dissolved completely. This will create a simple syrup.
Remove the syrup from heat and allow it to cool.
2. Prepare the Lemonade:
In a blender, combine the freshly squeezed lemon juice, the cooled simple syrup, the remaining 1 1/2 cups of cold water, and the ice cubes.
If you’re using lemon zest, add it to the blender at this point for an extra burst of lemon flavor.
3. Blend:
Blend everything together on high until the mixture is smooth and slushy. If it’s too thick, you can add a little more cold water to achieve your desired consistency.
4. Serve:
Pour the frozen lemonade into glasses. If you like, garnish with lemon slices or a sprig of mint for a nice touch.