Start by preheating the oven to 350°F. Make a parchment paper sling for a 9×5-inch loaf pan (or use two 8×4-inch loaf pans).
Inside of a large bowl, combine cake mix, pudding mix, eggs, sour cream, ⅓ cup lemon juice, milk, and oil. Beat with a mixer on medium until smooth, about 2 minutes. Spoon batter into prepared loaf pan(s). Do not smooth the top.
Bake until a toothpick inserted into the center comes out clean, which should take 60 to 65 minutes. If necessary, you can cover loosely with foil during the last 15 minutes of cooking to prevent overbrowning. If you are using 8×4-inch pans, bake for 45 to 50 minutes, covering with foil for the last 10 minutes if necessary. Cool in the pan on a wire rack for 20 minutes. Use the parchment overhang to lift bread from pan(s), and cool completely on the rack. Remove parchment paper.
Inside of a bowl, whisk together powdered sugar and 3 Tbsp. lemon juice until smooth. Add additional lemon juice or milk, ¼ tsp. at a time, to create a thinner icing. Spoon over loaf and let stand for 30 minutes before slicing. Top with Candied Lemon Slices, if desired.
