Heat oven to 350°F. Lightly grease a 9×13-inch baking dish.
Combine crushed pretzels, melted butter, and granulated sugar until evenly moistened.
Press mixture firmly into the dish. Bake 10 minutes, then cool completely.
Beat softened cream cheese, powdered sugar, and vanilla until smooth and fluffy.
Fold in whipped topping. Spread over cooled crust, sealing to the edges to prevent leaks.
Whisk lemon pudding mix with cold milk and lemon zest for 2 minutes until thickened.
Rest pudding 5 minutes, then spread gently over the cream layer.
Chill until fully set, at least 2 hours or overnight for the cleanest slices.
Top with remaining whipped topping and sprinkle with crushed pretzels. Slice and serve cold.