At this point, there are two ways to proceed. If you have a powerful blender, blend water, lemon juice, mint, and ice into a liquid similar to a slushie. If, instead, you believe that your blender will not survive crushing the ice, just crush the mint inside a cup with the lemon juice and the sugary water using a cocktail muddler tool, then strain the liquid and dilute it with the remaining water and serve over ice.
1.5 cup lemon juice, 1 cup fresh mint leaves, plus more to decorate, ice, about 3 cups