Preheat oven to 350°F. Grease or line an 8x8 baking dish with parchment paper.
In a large bowl, whisk together melted butter and sugar. Add sourdough discard, buttermilk, egg, and vanilla. Mix until smooth.
In a separate bowl, combine sifted flour, baking powder, baking soda, and salt. Stir into wet ingredients just until combined.
In a small bowl, toss blackberries with flour, sugar, and lemon zest.
In another bowl, mix flour, brown sugar, and cinnamon. Cut in cold butter until crumbly.
Spread half the batter into prepared pan. Add blackberry mixture evenly over top. Spoon remaining batter over berries.
Sprinkle crumb topping evenly over the cake.
Bake for 45–50 minutes, or until center is set and a toothpick comes out clean (a little berry juice is fine).
Cool for 15–20 minutes before slicing and serving.