In a medium saucepan over medium heat, combine the sugar and water for the simple syrup. Heat, stirring occasionally until the sugar is dissolved. Remove from heat and cool.

Meanwhile, in a small saucepan, combine blackberries, 2 tablespoons of sugar, and 2 tablespoons of water. Heat on medium heat, stirring occasionally until the blackberries are softened and smash easily, making a blackberry sauce of sorts. Remove from heat and allow to cool slightly before pressing through a fine mesh strainer (over a bowl or other clean receptacle) to remove the seeds.

Once the simple syrup and blackberry puree have cooled, combine with fresh squeeze lemon juice and water in a large pitcher. Stir to mix well and then refrigerate until cold.

Serve over ice with lemon slices or wedges, blackberries and mint leaves, if desired.