Preheat oven to 350 degrees F (175 degrees C). Grease 2 loaf pans.
Combine cake mix, pudding mix, oil, eggs, sour cream, milk, and 6 tablespoons lemon juice into bowl of stand mixer; beat for 2 minutes and pour into prepared loaf pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 50 minutes. Cool in the pans for 20 minutes before removing from pans to cool completely on a wire rack.
Whisk confectioners' sugar and 3 tablespoons lemon juice together in a bowl until smooth; spoon evenly over the loaves and let set before slicing, about 30 minutes.