Juice the lemons using a citrus reamer or juicer until you have about half a cup of fresh lemon juice, then set aside.
In a small bowl, combine the sugar with the water and stir until the sugar is completely dissolved to create a simple syrup.
Pour the fresh lemon juice into the blender, add the cooled simple syrup, and blend briefly to combine.
Add the ice cubes to the blender and start blending on low speed, then increase to high until the mixture is slushy and smooth, about 30-45 seconds.
Stop the blender and check the texture; it should be icy and scoopable but not completely icy like a snow cone. If needed, add a few more ice cubes and blend again for a few seconds.
Pour the lemonade slushie into glasses and serve immediately with optional lemon slices or mint for garnish.