Preheat oven to 350ºF. Grease a 13x9-inch baking dish.
In a large mixing bowl, combine the white cake mix, instant lemon pudding mix, lemonade drink mix packets, sour cream, eggs, water, and oil. Mix with a hand mixer or whisk just until combined and smooth.
Pour the batter into the prepared pan. Bake 45-55 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely before frosting.
Gently pierce holes half way down the cake with a fork. In a small bow, whisk together lemon zest and juice and sweetened condensed milk. Pour the mixture evenly over the cake. Cool completely.
In a stand mixer or bowl with a hand mixer, whip cream cheese until smooth. Add vanilla extract and powdered sugar and whip again until incorporated well and smooth. Scrape down the edges of the bowl as needed.
Gradually beat in the heavy whipping cream. When stiff peaks form (mixture holds its shape), the frosting is complete.
Spread the icing all over the cake. Slice and serve.