Preheat the oven to 350°F. Grease and flour an 8x5-inch loaf pan.
In a large mixing bowl or stand mixer, beat together: 3/4 cup (1 1/2 sticks) unsalted butter, room temperature, 1/4 cup vegetable oil, 1 cup sugar, Zest of 2 lemons. Beat on medium speed for about 4 minutes, until the mixture is very light and fluffy.
Add 4 large eggs, one at a time, mixing well after each addition. Then mix in 2 teaspoons pure vanilla extract.
In a separate bowl, whisk together: 2 cups all-purpose flour (spooned and leveled), 1 1/2 teaspoons baking powder, 1/2 teaspoon salt
In a small bowl, stir together: 1/4 cup buttermilk, room temperature with the juice of 1 lemon.
Add the dry and wet ingredients to the batter in stages: Mix in 1/3 of the flour mixture, just until combined. Add half of the buttermilk-lemon mixture, mix gently.
Add another 1/3 of the flour, then the remaining buttermilk mixture, and finally the last 1/3 of the flour, mixing just until no dry streaks remain. Do not overmix.
Pour the batter into the prepared pan and smooth the top. Bake for 50–60 minutes, or until a toothpick inserted in the center comes out clean. If the top browns too quickly, tent loosely with foil (make sure it doesn’t touch the batter).
Let the loaf cool in the pan for 20 minutes, then remove it from the pan and transfer to a wire rack to cool completely.
Make the glaze.In a small bowl, whisk together: 2 cups powdered sugar, 2 to 3 tablespoons lemon juice ( added gradually).
Stir until the glaze is thick but pourable. It should fall in ribbons when you lift the spoon.
Once the loaf is cool, drizzle the glaze over the top and let it set before slicing.