Preheat oven to 375 degrees F (190 degrees C). Spray a 9x9-inch baking pan with cooking spray.
Spread the blackberries into the prepared baking pan, and sprinkle with white sugar; drizzle with lemon juice. In a bowl, mix the lemon-poppy seed muffin mix, egg, milk, and cinnamon, and stir until moistened. It's okay to leave lumps in the batter. Pour the batter over the blackberries.
Place the butter and brown sugar into a bowl, and mix with an electric mixer on medium speed until the mixture resembles coarse crumbs. Spread this mixture over the batter in the pan.
Bake in the preheated oven until the topping is browned and the blackberries are bubbling, about 1 hour. Allow to stand for 20 minutes before serving.