Preheat oven to 350°F. Coat a 9-by-13-inch baking dish with cooking spray.
Combine 1⅓ cups blackberries, 1⅓ cups blueberries, 1⅓ cups raspberries, 3 tablespoons sugar and 1 tablespoon lemon juice in the prepared baking dish; gently toss and spread in an even layer.
Sprinkle the cake mix evenly over the berry mixture. Drizzle the melted butter evenly over the cake mix, making sure there are minimal dry spots.
Cover with foil and bake until the berries are bubbling, about 25 minutes. Remove the foil and continue baking until the topping is golden and set, 25 to 35 minutes more. Let cool for 10 minutes before serving.
