Preheat your oven to 350℉. Spray or grease a 1 pound 8.5×4.5″ baking pan. NOTE: for easier removal, fit the loaf pan with parchment paper with some overhang on the long side of the pan. You can easily lift the cooled cake out with the parchment paper overhang! In a medium mixing bowl, mix together the flour, baking powder, salt, and sugar. Use a spatula to scrape the sides down and mix until no flour streaks show.
1½ cups all-purpose flour, 1 teaspoon baking powder, ¼ teaspoon salt, 1 cup sugar
In a separate large mixing bowl, mix the softened butter, vanilla, eggs, oil, milk, lemon zest, and lemon juice until well combined.
1 cup butter, 1 teaspoon vanilla extract, 3 large eggs, 2 tablespoon vegetable oil, ¼ cup milk, 2 tablespoon lemon zest, 2 tablespoon lemon juice
Add the dry ingredients in two to three portions into the wet ingredients, mixing until just combined with each portion (this prevents the mixer from slinging flour everywhere!). Be sure to scrape the bowl sides down with a spatula as you mix.
Pour the lemon loaf cake batter into the baking pan and spread evenly. Bake in the preheated oven for 1 hour to 1 hour 10 minutes, or until the loaf cake is golden brown on top with a crack down the middle.
Set on a cooling rack to cool for about 45 minutes while you make the lemon drizzle icing.