Step 1: Preheat your oven to 350°F (175°C). Lightly grease a 9x5-inch loaf pan and line it with parchment paper, leaving an overhang on the sides to easily lift the cake out.
Step 2: In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
Step 3: In a large bowl, using a stand mixer or electric hand mixer, cream the softened butter and granulated sugar together on medium-high speed for about 3 minutes, until light and fluffy.
Step 4: Beat in the 1/4 cup fresh lemon juice and lemon zest until well combined.
Step 5: Add the eggs one at a time, beating well after each addition. Scrape down the sides of the bowl as needed to ensure all ingredients are thoroughly incorporated.
Step 6: With the mixer on low speed, gradually add the flour mixture in three batches, alternating with the 1/2 cup whole milk in two batches. Begin and end with the flour mixture. Mix until just combined, being careful not to overmix the batter.
Step 7: Pour the batter evenly into the prepared loaf pan and smooth the top with a spatula. Bake for 65 to 70 minutes, or until a wooden skewer or toothpick inserted into the center comes out clean.
Step 8: While the cake cools slightly in the pan for 10-15 minutes, prepare the glaze. In a small bowl, whisk together the powdered sugar, 2-3 tablespoons fresh lemon juice, and 1-2 tablespoons milk until smooth and pourable.
Step 9: Once the cake has cooled completely on a wire rack, drizzle the lemon glaze generously over the top. Allow the glaze to set before slicing and serving.