In large saucepan over medium-high heat, combine blackberries, sugar, corn starch, cinnamon and lemon juice. Cook, stirring constantly, until mixture thickens and comes to a boil (about 5 minutes). Boil and stir 1 minute.
Remove from heat and transfer to a greased 9x9-inch baking dish. Set aside.
In medium mixing bowl, combine baking mix and butter. Using a pastry blender or two forks, cut butter into baking mix until mixture resembles fine crumbs. Stir in milk.
Drop dough by spoonfuls onto warm fruit mixture. Bake in a preheated 400°F oven 25-30 minutes or until cobbler is golden brown and bubbly.