Preheat the oven to 350°F (175°C).
Peel and slice the apples, placing them in a large mixing bowl. Toss with lemon juice, Splenda, cinnamon, and nutmeg. Transfer the apple mixture to the prepared baking dish.
In another bowl, combine the oats, flour, and a pinch of salt. Add the cold butter cubes and use a pastry cutter or your fingers to work the butter into the dry ingredients until it forms a crumbly texture. Stir in the chopped nuts if desired.
Sprinkle the oat topping evenly over the apples.
Bake for 35-40 minutes, or until the apples are tender and the topping is golden brown.
Allow to cool for a few minutes before serving.