Preheat your oven to 350°F (177°C) and generously grease a 9×5-inch or 8×4-inch loaf pan, ensuring even coverage for easy release.
In a medium-sized mixing bowl, whisk together the all-purpose flour, baking powder, and salt to evenly distribute the dry ingredients. Set this aside.
Using a large mixing bowl and an electric mixer, blend the softened butter, vegetable oil, and sugar on medium-high speed until the mixture becomes pale and fluffy, about 4 to 6 minutes. Periodically scrape down the sides of the bowl to ensure thorough incorporation.
Add the eggs one at a time, beating well after each addition. Mix in the fresh lemon juice, zest, and vanilla extract, continuing to blend on medium-high speed until the mixture is smooth and aromatic.
Gradually incorporate the dry ingredients in three portions, alternating with the milk in two portions. Begin by mixing in a third of the dry ingredients until almost combined. Add half the milk and mix just until blended. Repeat this process with the next third of dry ingredients and the remaining milk. Finally, fold in the remaining dry ingredients, taking care not to overmix.
Pour the batter into your prepared loaf pan, smoothing the top with a spatula for an even bake. Place in the preheated oven and bake for 45-55 minutes, or until the loaf is golden brown and a toothpick inserted into the center comes out with only a few moist crumbs.
Once baked, let the loaf rest in the pan for about 15 minutes. Then, carefully transfer it to a wire rack to cool.
To prepare the lemon syrup, mix the lemon juice and powdered sugar in a small bowl until fully dissolved. While the cake is still warm, drizzle the syrup over it, allowing it to soak into the loaf. Let the cake cool completely before icing.
For the lemon icing, whisk together the powdered sugar, lemon juice, and heavy cream until the mixture is smooth and glossy. Spoon the icing over the cooled cake, spreading it evenly across the top. Let the icing set before slicing and serving.
Enjoy this luscious lemon loaf cake, perfect for a refreshing treat!