Preheat oven to 375°F.

Topping:

Combine flour, both sugars, salt, cinnamon, and pecans in a medium bowl. 

Cut butter or margarine in with a pastry cutter or your fingers, until well blended and the mixture crumbles coarsely. It should hold together when you pinch it. Refrigerate until ready to use.

Crisp:

Put apples, blackberries, and sugar in a medium-sized bowl. 

In a small bowl, dissolve cornstarch in lemon juice. Using a rubber spatula, gently combine the mixture with fruit.

Pour fruit into a greased 8- or 9-inch square glass or ceramic baking dish. Set the pan on a baking sheet to catch overflowing juices. 

Top fruit with half of topping. Do not press down. The topping should be light and crumbly. Keep remaining half of topping refrigerated.

Bake at 375°F for 20 minutes. 

After 20 minutes, sprinkle remaining topping over crisp. Continue baking 25 to 35 minutes more, until apples are tender when pierced with a knife, topping is crisp, and juices are bubbling. 

Cool for 20 to 30 minutes. Serve warm. 

Optional: For a dairy dessert, serve with a scoop of vanilla ice cream.