Preheat your oven to a toasty 325 degrees F (165 degrees C) and gently grease a 9-inch springform pan.
Mix together the graham cracker crumbs and butter until well combined, then press the mixture onto the bottom of the pan.
Bake at the set temperature until beautifully golden, approximately 10 minutes. Take out and let it cool to perfection.
Once the crust has cooled, use an electric mixer to beat the cream cheese in a large mixing bowl until smooth. Mix in the sweetened condensed milk. Add the eggs one at a time, ensuring you beat well after each addition. Finally, incorporate the lemon juice until fully combined, then pour the filling into the cooled crust.
Bake the cheesecake in the preheated oven for 45 to 55 minutes, or until it springs back when lightly touched. Allow it to cool completely on a wire rack for about 1 hour.
After letting the cheesecake cool, combine raspberries, sugar, water, and cornstarch in a small saucepan. Boil, stir, and cook until thickened for 1 to 2 minutes. Remove from heat and allow to cool for 10 to 15 minutes before using.
Drizzle the chilled raspberry filling over the chilled cheesecake and refrigerate for 1 hour.
In a medium bowl, combine milk and lemon pudding mix until smooth. Gently fold in whipped topping. Spread over the raspberry layer, cover, and refrigerate for 8 hours or overnight. Remove the sides of the springform pan before serving.