Make the simple syrup: Over medium heat, combine the ½ cup sugar and ½ water in a small saucepan. Bring to a boil, then reduce to a simmer. Cook until the sugar is completely dissolved. Allow the syrup to cool completely.
Add the lemon juice, lemon zest, water, simple syrup, and ice into a high powered blender. Blend on high for 1 minute until it forms a "slushy". Add ¼ cup more water if too thick or add a few more ice cubes if too thin.
Garnish with lemon zest and slices, if desired. Serve immediately.