Set oven temperature to 350°F. Butter a 9-by-5-inch loaf pan.
Mix the flour, baking powder, and salt in a bowl and put it aside.

Beat the eggs, sugar, and banana together in the bowl of your electric mixer until they are smooth. Beat in the milk, lemon juice, and vegetable oil until smooth.
When a toothpick inserted in the middle comes out clean, bake the bread for 55 to 60 minutes after pouring the batter into the prepared loaf pan. After five minutes of cooling, transfer to a wire rack to finish cooling.
Whisk together the butter, lemon juice, and powdered sugar until the glaze becomes white and thick. Cover the top of the cooled loaf with this frosting made with lemon juice.