Preheat the oven to 350 degrees F (175 degrees C). Coat the bottom of a 10-inch springform pan with cooking spray.

Reserve 1 cup cake mix for crumb topping; place remaining in a large bowl. Add 3/4 cup plus 1 tablespoon milk, oil, and eggs to bowl; beat using an electric mixer until batter thoroughly combined, about 2 minutes. Pour into the prepared pan.

Whisk melted butter and vanilla extract together in a bowl; stir in reserved 1 cup cake mix until crumbly. Sprinkle over cake batter.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Cool in the pan until room temperature.

Beat cream cheese, 1/3 cup confectioners' sugar, lemon juice, and lemon zest together in a bowl until smooth and creamy. Beat cream and remaining 1/3 cup confectioners' sugar together in a separate bowl using an electric mixer until stiff peaks form. Fold cream cheese mixture into whipped cream.

Remove cake from springform pan. Cut cake into 2 layers, horizontally, using a serrated knife. Spread cream filling onto bottom cake layer; place top layer over filling. Refrigerate cake for at least 4 hours. Dust cake with more confectioners' sugar before serving.