To make the cake, first combine the boxed mix, egg whites, lemon pudding mix, and water in a large bowl.
Bake the cake for 22-26 minutes, until it is done. Allow the cake to cool for at least an hour before frosting it.
To make the frosting, beat the milk and vanilla pudding mix in a large mixing bowl with a hand mixer for 2-3 minutes until smooth.
Assemble the cake. Once it has cooled, spread frosting on top and refrigerate for at least 2 hours so it will be chilled.
Make sure all of your ingredients are at room temperature before beginning, especially the eggs. Room temperature ingredients mix together more easily and produce a better cake.