Preheat the oven to 350°F (177°C)
In a large bowl, whisk together the flour, baking powder, baking soda, and salt. Set the mixture aside.
In a medium bowl, combine sugar, vanilla extract, olive oil, milk, lemon juice, and lemon zest, whisking them together.
Combine the dry ingredients from the medium bowl with the wet ingredients in the large bowl, mixing them together until they are fully combined.
Transfer the batter to a greased 8-inch round cake pan, spreading it evenly.
Bake for approximately 35 minutes, or until the top is golden and a toothpick inserted into the center comes out clean. Remove the cake from the oven and let it cool.
While the cake is cooling prepare the lemon glaze. Whisk the ingredients until smooth. If needed, adjust the thickness by adding more lemon juice to thin it or more powdered sugar to thicken it.
After the cake has cooled, take it out of the pan and apply the glaze. Pour it over the top and spread it across the top and down the sides. Let the glaze set for a while before slicing and serving the cake.