Heat 3/4 cup sugar and 1/2 cup water in a small saucepan over medium heat. Cook and stir until sugar has dissolved, about 2 minutes. Let cool.

Place blackberries and remaining 2 tablespoons of sugar in a blender; blend until smooth.

Combine simple syrup, blended blackberries, remaining 4 cups of water, and lemon juice. Place a fine-mesh sieve over a pitcher and pour lemonade into the pitcher; discard solids. Serve over ice.