Place the ¾ cup water and ¾ cup sugar in a sauce pan. Heat over medium low heat, stirring often, until the sugar is dissolved. Remove from heat and let cool. Juice the lemons, and put the juice in a pitcher. Add the 4 ½ cups water and the cooled simple syrup. Stir well.
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.
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