Heat the sugar and water in a saucepan over medium heat. Stir occasionally and cook until all of the sugar is dissolved.
Puree the blackberries in a blender or food processor. Mine were frozen, so I added a bit of the sugar water to the berries to blend them easier.
Mix sugar water, berry puree and lemon juice in a half gallon pitcher. Fill with ice.
Serve over ice.
Notes
Feel free to add as many blackberries as you have/want. More blackberries will result in a thicker, richer feeling lemonade. Fewer will be lighter and still delicious.