Begin by blending the fresh strawberries in a blender until smooth. You can add a little bit of the cold water to help with blending if needed.
In a separate bowl, combine the freshly squeezed lemon juice and granulated sugar. Stir until the sugar is completely dissolved.
Add the strawberry puree to the lemon juice mixture and mix well.
Pour this mixture into the blender, add the ice cubes, and the remaining cold water. Blend on high until smooth and slushy in texture. If it's too thick, you can add a bit more water and blend again.
Taste the frozen lemonade and adjust the sweetness by adding more sugar or a splash more lemon juice if desired.
Pour into chilled glasses and garnish with fresh mint leaves if using.