Preheat oven to 350°F. Butter and flour a 10 cup bundt pan.
In a large mixing bowl, beat together cake mix, lemon pudding, lemon oil, eggs, water, and vegetable oil. Beat on medium speed for 2-3 minutes
Pour batter into the prepared cake pan.
Bake for 45 minutes or until a toothpick inserted into the center of the cake comes out clean.
Allow cake to cool in the pan for 15 minutes, then invert the pan onto a cooling rack and remove cake from the pan to cool the rest of the way.
When the cake is cool, prepare the glaze.
Whisk together the powdered sugar, lemon juice, and milk until a thick glaze forms. Adjust the consistency by adding additional milk to thin or extra powdered sugar to thicken.
Place the cake, still on the cooling rack, over a covered surface (or over a sheet pan) for easy cleanup. Spoon or pour the glaze over the top of the cake, allowing it to drizzle down the sides a bit. Work quickly as the glaze will begin setting quickly.
Allow the glaze to set, about 20 minutes, before cutting and serving.