In a large saucepan, bring 2 cups water and sugar to a boil. Boil for 2 minutes, stirring occasionally. Remove from the heat. Stir in the lemon juice, zest and remaining water; cool slightly.
In a blender, combine 1 cup of lemon mixture and the blackberries; cover and process until blended. Strain and discard seeds. Pour blackberry mixture and remaining lemon mixture into a pitcher; stir well. Refrigerate until chilled. Serve in chilled glasses over ice.