Preheat your oven to 375°F
Grease a 9x9-inch baking dish and set aside
In a large bowl, combine the sliced apples, blackberries, granulated sugar, flour, cinnamon, nutmeg, and lemon juice
Toss until the fruit is evenly coated
Transfer the mixture to the prepared baking dish
In another bowl, mix together the oats, flour, brown sugar, cinnamon, and salt for the crisp topping
Add the cold cubed butter and use your fingers or a pastry cutter to work it into the dry ingredients until the mixture resembles coarse crumbs
Sprinkle the crisp topping evenly over the fruit mixture in the baking dish
Bake in the preheated oven for 35 to 40 minutes, or until the filling is bubbly, and the topping is golden brown
Remove from the oven and let it cool slightly before serving
Serve warm with a scoop of vanilla ice cream or a dollop of whipped cream, if desired