Place a rack in the middle position in the oven and preheat to 375 degrees F (190 degrees C). Spray a 9x13-inch baking dish with cooking spray. Line a baking sheet with aluminum foil.

Combine apples, dried cranberries, 1/2 cup flour, 1/2 cup white sugar, lemon juice, 1 tablespoon cinnamon, and 1/2 teaspoon nutmeg together in a bowl until apples and cranberries are well-coated; spread filling into the prepared baking dish.

Mix oats, brown sugar, 1/2 cup flour, 1/2 cup white sugar, butter, 1/2 teaspoon cinnamon, 1/2 teaspoon nutmeg, baking soda, baking powder, and salt together in a bowl using your hands until well-mixed; sprinkle over the filling. Place baking dish on the prepared baking sheet.

Bake in the preheated oven until filling is bubbling and topping is golden brown, 55 to 60 minutes. Remove baking dish from oven and cool crisp for 15 minutes before serving.