Place the blackberries and lemon juice into a saucepan over medium heat. Cook, mashing them with a masher, for about 5-7 minutes. Strain the mixture through a very fine wire mesh strainer. Set aside to cool.
Combine the zest of the lemon and the white sugar together with your fingers until it's well combined and the sugar is fragrant. Set aside.
Cream the butter with a hand mixer until creamy and smooth. Add the fragrant sugar and blend until well combined. Add the eggs, one at a time and mix thoroughly. Add 1/2 cup of blackberry juice and blend until well combined.
Pour into a small saucepan and cook over medium heat, stirring often, until thickened, about 10 minutes at about 170 degrees. Remove from heat and let cool before pouring it into a container. Side Note: If you accidentally overcook the sauce, it may curdle a bit. Simply pour through the fine mesh strainer to remove any clumps.
Serve over crepes, pancakes & waffles, toast, ice cream, muffins, or sugar cookies. Store, well sealed, in the refrigerator. Enjoy.