Preheat the oven to 350°F. Grease a 9 × 5-inch loaf pan and line it with parchment paper, leaving an overhang. Whisk together the flour, baking powder, and salt in a medium bowl.
Beat the softened butter, granulated sugar, and lemon zest in a large bowl for 2–3 minutes, until light and creamy.
Add the eggs one at a time, beating after each addition. Mix in the vanilla extract.
Mix in the sour cream and 2 tablespoons lemon juice. Add the dry ingredients and mix on low speed just until no dry flour remains. Avoid overmixing.
Spread the batter evenly in the prepared loaf pan. Bake at 350°F for 50–60 minutes, until the top is golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the loaf cool in the pan for 15 minutes. Lift it out using the parchment overhang and transfer it to a wire rack to cool completely.
Whisk the powdered sugar with 1 1/2 tablespoons lemon juice. Add a little more juice, up to 2 tablespoons total, until the glaze is thick but pourable.
Drizzle the glaze over the completely cooled loaf, allowing some to run naturally down the sides.
Let the glaze set for about 10 minutes before slicing the loaf with a sharp knife.
Slice and serve. Enjoy with coffee, tea, or fresh berries.