Preheat the oven to 325°F (160°C).
Prepare the crust by mixing crushed graham crackers and melted butter in a bowl until combined.
Press the graham cracker mixture into the bottom and halfway up the sides of a 9-inch springform pan.
In a bowl, mix diced apples with lemon juice, 1/4 cup sugar, and cinnamon. Set aside.
In a large mixing bowl, beat softened cream cheese, remaining sugar, and vanilla until smooth.
Add eggs one at a time, mixing well after each addition until just combined.
Stir in sour cream until fully combined, ensuring a smooth consistency.
Pour half of the cheesecake batter into the prepared crust, spreading it evenly.
Layer the apple mixture evenly over the cheesecake batter.
Pour the remaining cheesecake batter on top, smoothing it out gently.
Prepare the crumble by combining oats, brown sugar, flour, butter, and salt until crumbly.
Sprinkle the crumble evenly over the top of the cheesecake layer.
Bake for 50-60 minutes or until the edges are set but the center still has a slight jiggle.
Turn off the oven, crack the door, and let the cheesecake cool in the oven for about an hour.
Remove from the oven and let it cool completely at room temperature before refrigerating for at least 4 hours.
Once chilled, carefully remove the cheesecake from the springform pan and slice into pieces for serving.