In a saucepan over medium-high heat, combine the sugar, frozen berries, and ½ cup water. Bring the mixture to a gentle boil, the cook for about 10 minutes, until the berries soften and burst.
Pour the syrup mixture into a blender and carefully blend until smooth. Place 2 cups of ice in a pitcher or measuring cup. Place a fine mesh strainer over the ice and strain the berry mixture (to catch all the small seeds) over the ice to cool it down quickly.
Combine the ice/syrup mixture, lemon juice, and 3 cups of cold water in a pitcher. Stir to combine and add more water if needed. Enjoy!