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

In a large bowl, combine the remaining cake mix, ¾ cup plus 1 tablespoon of milk, vegetable oil, and eggs. Beat with an electric mixer for about 2 minutes until well combined. Pour the batter into the prepared pan.

In another bowl, whisk together the melted butter and vanilla extract. Stir in the reserved 1 cup of cake mix until you have 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. Let the cake cool in the pan until it reaches room temperature.

In a bowl, beat the cream cheese, ⅓ cup confectioners' sugar, lemon juice, and lemon zest until smooth.

In another bowl, whip the heavy cream with the remaining ⅓ cup of confectioners' sugar until stiff peaks form. Gently fold the cream cheese mixture into the whipped cream.

Carefully remove the cake from the springform pan. Use a serrated knife to slice the cake horizontally into two layers.

Spread the cream filling evenly over the bottom layer, then place the top layer over it.

Refrigerate the cake for at least 4 hours.

Before serving, dust the top of the cake with extra confectioners' sugar.