Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan.
In a large mixing bowl, combine the lemon cake mix, water, vegetable oil, and eggs.
Add 2 tablespoons of fresh lemon juice and 1 tablespoon of lemon zest to the batter.
Using an electric mixer, beat the mixture on medium speed for 2 minutes until smooth.
Pour the batter evenly into the prepared baking pan.
Bake in the preheated oven for 28 to 32 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the lemon glaze by mixing 1 cup powdered sugar with 2 tablespoons fresh lemon juice until smooth.
Remove the cake from the oven and allow it to cool for 10 minutes in the pan.
Poke holes all over the warm cake using a fork or skewer and pour the lemon glaze evenly over the top.
Let the cake cool completely before slicing and serving.