Preheat the oven to 325 degrees F (165 degrees C). Lightly grease a 9-inch springform pan.
Combine graham cracker crumbs and butter in a small bowl. Press into the bottom of the prepared pan.
Bake in the preheated oven until golden, about 10 minutes. Remove from the oven and let cool completely.
While crust is cooling, beat cream cheese using an electric mixer in a large mixing bowl until smooth. Beat in sweetened condensed milk. Add eggs, one at a time, beating well after each addition. Beat in lemon juice until well combined. Pour filling into the cooled crust.
Bake in the preheated oven until cheesecake springs back when lightly touched, 45 to 55 minutes. Let cool completely on a wire rack, about 1 hour.
While cheesecake is cooling, stir raspberries, sugar, water, and cornstarch together in a small saucepan. Bring to a boil; cook and stir until thickened, 1 to 2 minutes. Remove from heat and let cool completely, 10 to 15 minutes.
Pour cooled raspberry filling over cooled cheesecake. Refrigerate for 1 hour.
Pour milk into a medium bowl for topping. Whisk in lemon pudding mix until smooth. Gently fold in whipped topping. Spread on top of raspberry layer. Cover and refrigerate 8 hours to overnight. Remove sides of springform pan when ready to serve.
