Preheat the oven to 350°F. Grease and flour a 9×5-inch loaf pan.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat the butter and sugar until light and fluffy.
Add eggs one at a time, beating well after each addition. Mix in lemon zest and lemon juice.
Gradually add the dry ingredients to the wet ingredients alternately with milk, starting and ending with the dry ingredients.
Pour the batter into the prepared pan and bake for 50 minutes, or until a toothpick inserted into the center comes out clean.
Whisk together powdered sugar and lemon juice until smooth. Start with 1 tablespoon of lemon juice and adjust consistency as needed by adding more. Drizzle over cooled loaf.