Step 1: Cook lasagna noodles according to package directions until al dente. If using no-boil, set aside. Drain cooked noodles and rinse with cold water to prevent sticking; lay flat on parchment paper or a clean kitchen towel.
Step 2: To make the apple filling, combine sliced apples, brown sugar, granulated sugar, lemon juice, cinnamon, nutmeg, and salt in a large pot or deep skillet. Cook over medium heat, stirring occasionally, for 10-15 minutes, until apples soften but retain some bite. In a small bowl, whisk cornstarch and cold water until smooth; stir into the apple mixture. Cook for 2-3 minutes, until the sauce thickens. Remove from heat and let cool slightly.
Step 3: For the cheesecake filling, beat softened cream cheese in a large bowl with an electric mixer until smooth. Add powdered sugar, vanilla extract, and salt; beat until well combined. Gradually beat in heavy cream until the mixture is light, fluffy, and holds soft peaks.
Step 4: To prepare the crumb topping, combine flour, brown sugar, granulated sugar, cinnamon, and salt in a medium bowl. Add cold, diced butter and cut into the dry ingredients with your fingertips or a pastry blender until coarse crumbs form. Set aside.
Step 5: Preheat oven to 375°F (190°C). Lightly grease a 9×13 inch baking dish. Spread about 1/4 cup of the cooled apple filling evenly on the bottom of the dish. Lay 3-4 lasagna noodles over the apple base, overlapping slightly. Spread half of the cheesecake filling evenly over the noodles. Top with half of the remaining apple filling. Repeat with another layer of noodles, the remaining cheesecake filling, and the remaining apple filling. Finish with a final layer of noodles.
Step 6: Evenly sprinkle the prepared crumb topping over the final layer of noodles. Cover the baking dish loosely with aluminum foil. Bake for 30 minutes. Remove the foil and continue to bake for another 15-20 minutes, or until the crumb topping is golden brown and the filling is bubbly.
Step 7: Remove the Layered Apple Pie Lasagna from the oven and let it cool on a wire rack for at least 20-30 minutes before slicing and serving. Serve warm, optionally with vanilla ice cream, whipped cream, or caramel sauce.