Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish. Chill beaters of an electric mixer and a metal or glass mixing bowl in the freezer.
Combine flour, 1/2 cup confectioners' sugar, butter, and lemon juice with 2 forks in a large bowl until thoroughly combined; press mixture into bottom of prepared baking dish.
Bake crust in the preheated oven until firm and lightly golden brown, 20 to 25 minutes. Let crust cool completely.
Whisk pudding mix and milk in a large bowl for 2 minutes; allow to stand until softly set, about 3 more minutes.
Beat cream, sour cream, 2/3 cup confectioners' sugar, and vanilla extract in the chilled bowl, using the chilled beaters, until mixture is thick and fluffy, 3 to 5 minutes. Mixture should form stiff peaks when beaters are lifted straight up. Refrigerate cream mixture for 20 minutes to continue to thicken.
Spoon lemon pudding in an even layer over the crust and top with whipped cream mixture in a layer; sprinkle with lemon zest.