Add blackberries, sugar and 2 cups of water to a pan and place over medium- high heat. Cook, stirring occasionally until mixture comes to a boil. Lower heat to a simmer and cook 5 minutes. Allow mixture to come to room temperature and refrigerate until completely cool. Or place in the freezer for about 30-45 minutes or until cool.
Strain blackberries, adding syrup to a pitcher. Reserve blackberries for another use. Add lemonade concentrate and 6 cups of water to blackberry syrup and stir to combine.
Serve over ice and garnish with lemon slices and blackberries.