Preheat the oven to 350°F and prepare your ingredients.
Mix sugar and butter in a stand mixer until fluffy for about 4 minutes.
Add eggs, lemon juice, and lemon zest, blending until combined.
Whisk flour, salt, and baking powder in a separate bowl, then incorporate into the batter.
Mix in milk until the batter is well combined, scraping the bowl as needed.
Pour the batter into a lined loaf pan and bake for 40-45 minutes.
Cool the loaf for 15 minutes in the pan, then on a wire rack for another 15 minutes.
Whisk powdered sugar, lemon juice, and lemon zest for the icing.
Pour one-third of the icing over the loaf, let it set for 5 minutes, and repeat twice.
Slice the loaf with a bread knife and serve.
