Grease a 9-inch round or 9×5-inch loaf pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, combine the granulated sugar and lemon zest.
Add the softened butter to the lemon sugar and beat until fluffy, about 2 minutes. Mix in the oil and continue beating until everything comes together
Add the eggs one at a time, mixing gently after each. Stir in the vanilla extract and lemon juice.
Add the flour mixture in two batches, alternating with the buttermilk.
Gently fold everything together just until combined.
Transfer the batter into your prepared pan. Smooth the top and bake for 40–50 minutes if using a loaf pan or 28–35 minutes for a round pan.
Let the cake cool for 10 minutes in the pan before transferring it to a wire rack.
To make the glaze, whisk powdered sugar with lemon juice until smooth and pourable.
Drizzle over the warm cake so it soaks in slightly but still sets beautifully on top.
