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

Set aside 1 cup of the cake mix for the crumb topping. Place the remaining cake mix in a large bowl. Add ¾ cup plus 1 tablespoon of milk, the vegetable oil, and the eggs. Use an electric mixer to beat the mixture until thoroughly combined, about 2 minutes. Pour the batter into the prepared pan.

In a separate bowl, whisk together the melted butter and vanilla extract. Stir in the reserved 1 cup of cake mix until it forms a crumbly texture. Sprinkle this crumb mixture evenly over the cake batter.

Bake the cake in the preheated oven for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan until it reaches room temperature.

To prepare the filling, beat the cream cheese, ⅓ cup of confectioners' sugar, lemon juice, and lemon zest in a bowl until smooth and creamy. In a separate bowl, whip the heavy cream with the remaining ⅓ cup of confectioners' sugar using an electric mixer until stiff peaks form. Gently fold the cream cheese mixture into the whipped cream.

Carefully remove the cake from the springform pan. Using a serrated knife, slice the cake horizontally into two layers. Spread the cream filling evenly over the bottom layer, then place the top layer over the filling. Refrigerate the cake for at least 4 hours. Before serving, dust the top of the cake with additional confectioners' sugar.