- In a small bowl, stir together the 1 1/4 cups lemon juice, the orange juice and the 3/4 cup simple syrup. Set aside.
- In another small bowl, stir together the blackberry juice, the 1 teaspoon lemon juice and the 2 tablespoons simple syrup. Set aside.
- Put the ice cubes in a blender and add the lemon juice mixture. Using the ice crush feature of the blender or high speed, blend until smooth.
- Put 1 tablespoon of the blackberry puree into each of 4 glasses. Pour in the frozen lemonade, dividing evenly. Garnish each with a mint sprig and a few blackberries. Serve immediately.