In a large bowl, combine the lemon cake mix, lemon pudding mix, milk, oil, lemon juice, lemon zest, applesauce, and eggs. Whisk until smooth.
Pour the batter into the prepared Bundt pan. Bake for 40 minutes or until a toothpick inserted comes out clean.
To make the glaze, whisk together the powdered sugar and about 3 tablespoons of lemon juice in a small bowl. Add 1 tablespoon more lemon juice if needed to thin out the glaze.