Preheat oven to 350°F. Grease 9x13 baking pan.
Beat eggs in a large bowl, using an electric mixer. Add cake mix, pudding mix, water, and oil, and mix until well combined.
Pour the cake batter into a baking pan. Bake in the preheated oven for 30-35 mins, or until a toothpick inserted into the cake comes out clean. While the cake is baking, you can prepare a syrup.
To make soaking syrup: in a bowl, combine melted butter, lemon juice, water, and powdered sugar.
When the cake is done, poke holes all over the cake with a skewer (or a fork), then pour the soaking syrup over the warm cake. Let it cool completely in a pan before serving.