Step 1: Preheat your oven to 325°F (160°C). Grease and flour a 9x5-inch loaf pan, or spray with a baking spray with flour.
Step 2: In a large bowl, cream together the softened butter and granulated sugar with an electric mixer until light and fluffy, about 3-5 minutes. Scrape down the sides of the bowl as needed.
Step 3: Add the eggs one at a time, beating well after each addition until fully incorporated. Stir in the lemon zest.
Step 4: In a separate medium bowl, whisk together the flour, baking powder, and salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, alternating with the milk and starting and ending with the dry ingredients. Mix on low speed just until combined; do not overmix. Stir in the 1/4 cup fresh lemon juice.
Step 6: Pour the batter evenly into the prepared loaf pan.
Step 7: Bake for 60-70 minutes, or until a wooden skewer inserted into the center comes out clean. If the top browns too quickly, tent loosely with aluminum foil.
Step 8: Remove the cake from the oven and let it cool in the pan for 15-20 minutes before inverting it onto a wire rack to cool completely.
Step 9: While the cake cools, prepare the lemon glaze. In a small bowl, whisk together the powdered sugar and 1/4 cup fresh lemon juice until smooth. If the glaze is too thick, add a tiny bit more lemon juice; if too thin, add more powdered sugar.
Step 10: Once the cake is completely cool, drizzle the lemon glaze evenly over the top, allowing it to drip down the sides. Slice and serve.