Preheat the oven to 400° and place the rack in the middle position.
Line a 9-inch pie plate with the store-bought pie crust. Par-bake the crust in the preheated oven for 6 minutes, then remove it and set it aside.
In a large bowl, combine the sliced apples, lemon juice, lemon zest, brown sugar, granulated sugar, flour, salt, cinnamon, nutmeg, and vanilla extract. Gently toss the ingredients together, ensuring the apples are evenly coated. Let the mixture marinate for 10 minutes.
In another bowl, mix together the ingredients for the topping until you achieve different-sized crumbs. Using your hands works best for this step.
Once the apples have marinated, transfer them to the par-baked pie crust. Sprinkle the prepared topping over the apple filling.
Place the pie in the preheated oven at 400° for 15 minutes. Then, reduce the temperature to 350° and continue baking for an additional 40-45 minutes, or until the top is bubbly and slightly browned.
Halfway through baking, check the crust to ensure it is not burning. If necessary, cover the edges with foil to prevent burning.
Once baked, remove the pie from the oven and allow it to cool for at least 20 minutes before serving.
Serve slices of pie with whipped cream or ice cream, if desired. Enjoy!