Make the crust in a food processor. Pulse flour, salt and 2 tablespoons sugar until combined. Add butter and pulse until mixture resembles coarse meal. With machine running, add 1 cup ice water. Pulse until dough is crumbly but holds together when squeezed. Do not over-mix.
Divide dough into 2 disks. Wrap each tightly in plastic wrap. Refrigerate until firm, at least 1 hour.
Preheat oven to 400F degrees. Make filling in a large bowl. Toss together blackberries, apple slices, cornstarch, 1/2 cup sugar, lemon zest and lemon juice. On a floured work surface, roll out 1 disk to a 12x16-inch rectangle. Place in a 10x14-inch rimmed jelly roll pan.
Pour fruit mixture filling in the crust, then lightly brush edges of crust with water. On floured surface, roll out second disk to 11x15-inch rectangle and lay over fruit filling. Press along moistened edges to seal. Fold overhang under, tucking into the pan and crimp edges. With paring knife, cut slits on top to vent.
Reduce heat to 375F degrees. Place pie in oven and bake until crust is golden and juices are bubbling (about 50 minutes). Let cool on a wire rack for 1 hour. Serve warm or at room temperature.