Preheat the oven to 375 degrees F (190 degrees C). Generously grease a shallow 2-quart baking dish with 2 tablespoons butter, and set aside.
Grate apples into a bowl, and add lemon juice, cinnamon, cornstarch, white sugar, and brown sugar. Mix thoroughly, and transfer into the prepared baking dish.
Add oats, Grape Nuts, flour, white sugar, brown sugar, and melted butter into the bowl used for the apples, and stir thoroughly until everything is evenly coated with melted butter; spread mixture evenly over the apples.
Bake in the preheated oven until the apple layer has thickened, is bubbling around the sides, and topping is golden brown, about 1 hour.
Remove and let cool to warm before serving, or chill before serving if you prefer.