In a food processor (a bowl with a pastry blender works just fine too), combine all of the crisp topping ingredients (first 6 ingredients - up to the apples).
Pulse until the butter is the size of a pea and everything is blended. About 5-10 seconds of pulsing the machine. That's it. The topping is done.
Peel and core the apples cut them into 2 cm wedges and put them in a medium mixing bowl with the rinsed blackberries and sprinkle the lemon juice over the fruit.
Add the flour and brown sugar to the fruit and stir to coat reasonably evenly.
In a 2 quart (approximately) baking dish, lightly greased either with butter or cooking spray, dump in the apples and blackberries. Spread them out so it is even in your dish.
Gracefully dump the crisp topping onto the fruit and spread that out.
Bake in a 375 degrees F oven for 45 minutes. Turn the oven down to 350 degrees F if the apples aren't done then bake for an additional 10 minutes. If you are using less firm apples then reduce your baking time accordingly. Use your judgement.
I serve my apple crisp with custard from a can - it is delicious. Serve with vanilla ice cream if you prefer or if you are really up-market, make your own custard from scratch (or just call the stuff in the can creme anglaise to make yourself feel better).