01 - Preheat oven to 350°F. Grease and line a 9x5-inch loaf pan with parchment paper.
02 - Whisk together flour, baking powder, baking soda, and salt in a medium bowl. Set aside.
03 - Beat butter and sugar in a large bowl until light and fluffy, approximately 2 to 3 minutes.
04 - Add eggs one at a time into the butter mixture, beating well after each addition.
05 - Stir in lemon zest, lemon juice, and vanilla extract.
06 - Mix in half of the flour mixture gently, then add the milk. Follow with the remaining flour mixture and stir until just combined; avoid overmixing.
07 - Pour batter into the prepared loaf pan and smooth the surface evenly.
08 - Bake for 45 to 50 minutes, until a toothpick inserted near the center comes out clean.
09 - Allow cake to cool in pan for 10 minutes before transferring to a wire rack to cool completely.
10 - Whisk powdered sugar and lemon juice together until smooth and pourable; adjust consistency with additional lemon juice if needed.
11 - Drizzle icing over the cooled cake and allow it to set before slicing.