Heat the oven to 350°F (175°C). Grease the loaf pan and fit a parchment sling. Whisk flour, baking powder, baking soda, salt, and poppy seeds.
Rub lemon zest into granulated sugar until fragrant. Beat with softened butter for 3 minutes, scraping the bowl, until light and creamy.
Beat in eggs one at a time. Mix sour cream, milk, and batter lemon juice in a separate small bowl.
Add dry ingredients in three portions, alternating with the sour cream mixture. Mix on low just until combined, avoiding prolonged beating.
Spread batter evenly in the pan. Bake 50–60 minutes until a center skewer shows no wet batter and the top springs back gently.
If the loaf colors early, tent loosely with foil. Cool in the pan 15 minutes, then lift onto a rack and let cool completely.
Whisk powdered sugar with 1 tablespoon glaze lemon juice. Add the second tablespoon gradually until thick but pourable, rather than thin and watery.
Drizzle over the cool loaf and let settle before cutting. Use a serrated knife for even slices and keep the cut end covered during storage.
