In a mixing bowl, combine sliced apples, brown sugar, cinnamon, and lemon juice. Toss to coat and set aside.

In another bowl, beat the cream cheese and sugar until smooth. Add vanilla and mix well.

Add eggs one at a time, mixing well after each addition. Finally, stir in sour cream until combined.

In a bowl, mix flour, oats, brown sugar, and salt. Cut in cold butter until the mixture resembles coarse crumbs.

Preheat the oven to 325°F (160°C). Pour the cheesecake filling into the springform pan.

Layer the apple filling over the cheesecake mixture, then sprinkle the crumble topping evenly on top.

Bake in the preheated oven for 60 minutes or until the center is set. Turn off the oven and let the cheesecake cool in the oven for 1 hour.

Remove from the oven and refrigerate for at least 4 hours before serving.