Prep the pan and oven. Preheat oven to 350°F (175°C). Grease a 9x13-inch baking pan or line with parchment for easy removal.
Mix the cake batter. In a large bowl, combine cake mix, eggs, oil, and water.
Add the lemon zest for extra brightness. Beat until smooth and combined, about 2 minutes.
Bake the cake. Pour into the prepared pan and bake 25–30 minutes, or until the center springs back and a toothpick comes out clean. Don’t overbake—slightly underdone edges are better than dry cake.
Poke the cake. Let the cake cool for 10–12 minutes.
Using the handle of a wooden spoon or a thick straw, poke holes all over the surface, spacing them about 1 inch apart. Go deep but not through the bottom.
Make the lemon pudding. In a medium bowl, whisk the lemon pudding mixes with cold milk and lemon juice for 2 minutes until thickened but still pourable. Work quickly; instant pudding sets fast.
Fill the holes. Pour the pudding evenly over the warm cake, gently nudging it into the holes with a spatula.
Smooth the top. Chill for at least 30 minutes to set.
Make the cream cheese topping. Beat the softened cream cheese with powdered sugar, vanilla, and a pinch of salt until smooth. In a separate bowl, whip the cold heavy cream to medium-stiff peaks.
Fold the whipped cream into the cream cheese mixture until fluffy and uniform.
Top the cake. Spread the cream cheese mixture over the chilled cake in an even layer. Add a light sprinkle of lemon zest for fragrance and color.
Chill and serve. Refrigerate at least 2 hours, or overnight for clean slices and deeper flavor. Slice cold and serve as is, or garnish with fresh berries.