In a large bowl, toss together diced apples, grated apple, sugar, brown sugar, 1 tablespoon cinnamon, nutmeg, and lemon juice. Combine thoroughly, and pour the mixture into the bottom of your slow cooker and spread evenly.

In a medium bowl, whisk together the oats, flour, sugar, 1 teaspoon cinnamon, and salt.

Using your fingers or a pastry cutter, work the butter into the oat mixture until coarse crumbs form.

Sprinkle the oat mixture evenly over the apple mixture in the slow cooker.

Place the lid on the slow cooker and cook for four hours on high or seven hours on low, until the crust is a golden brown.

Serve hot or at room temperature with whipped cream or ice cream.