In a medium saucepan over medium heat, combine 1 3/4 cups sugar and 1 cup of water. Heat, stirring occasionally, until sugar is completely dissolved. Remove from heat and cool completely.

In a blender, combine blackberries with the remaining 2 tablespoons of sugar. Blend until pureed. Press blackberry puree through a fine mesh sieve to get as much liquid through as possible, then discard solids.

Combine the blackberry puree with the simple syrup, lemon juice, and water in a large pitcher. Stir well. Serve with ice, sliced lemons, and blackberries for garnish.