Preheat the oven to 350°F. Grease and flour a Bundt cake pan, or spray generously with nonstick baking spray.
In a large bowl, use an electric mixer on medium-high speed to beat together the cake mix, dry pudding mix, water, lemon juice, oil, and eggs for about 2 minutes.
Pour the batter into the prepared pan. Tap on the counter once or twice to release air bubbles. Bake for 40 minutes, or until a toothpick inserted in the cake comes out clean.
Cool for 10 minutes in the pan, then invert onto a wire rack to cool completely before glazing.
Whisk together the confectioners' sugar, 2 tablespoons of lemon juice, and the vanilla extract until you have a thick, pourable glaze. Add more lemon juice to thin, or more sugar to thicken.
Drizzle the glaze over the cooled cake. Let the glaze set, then slice and serve.