Preheat oven to 350°F (175°C) and grease a 9x13-inch baking pan.
Make the cake batter: In a large bowl, beat the eggs with an electric mixer. Add the cake mix, lemon pudding mix, water, and oil. Mix until smooth and well-combined.
Bake the cake: Pour the batter into the prepared pan. Bake in the preheated oven for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Prepare the soaking syrup: While the cake is baking, combine the powdered sugar, lemon juice, melted butter, and water in a bowl. Stir until smooth.
Poke holes and add the syrup: Once the cake is done, remove it from the oven. While it’s still warm, poke holes all over the cake using a skewer or fork. Pour the soaking syrup over the warm cake, making sure it soaks in.
Make the lemon topping: In a mixing bowl, beat together softened cream cheese, heavy cream, powdered sugar, and lemon zest until smooth and fluffy.
Cool and refrigerate: Allow the cake to cool completely in the pan. For the best texture, refrigerate the cake for 1-2 hours to let the syrup fully set.
Serve: Once chilled, spread the creamy lemon topping over the cake. Slice, serve, and enjoy the refreshing flavors of this Italian Lemon Cream Cake!