Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream the softened butter and granulated sugar together until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition.
Mix in the vanilla extract, lemon juice, lemon zest, and vegetable oil until combined.
Alternately add the flour mixture and milk to the wet ingredients, beginning and ending with the flour mixture. Mix until just combined; do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Run a knife around the edges of the cake, then invert it onto a wire rack to cool completely before serving.