Preheat oven to 350°F (175°C). Grease and flour a 9×13-inch baking dish.
In a large bowl, combine the cake mix, lemon pudding mix, eggs, oil, water, lemon juice, and lemon zest. Beat for about 2 minutes until smooth.
Pour the batter into the prepared pan and bake for 30-35 minutes or until a toothpick comes out clean.
While the cake is baking, whisk together powdered sugar and lemon juice (and milk if using) until smooth.
Once the cake is out of the oven, poke holes in the top and pour the glaze over it.
Allow the cake to cool completely before slicing. Garnish with extra lemon zest if desired.