Preheat the oven to 350F (180C fan forced). Line the bottome of two 8-inch round cake pans with parchment then grease and flour the sides. See recipe notes for pan size alternatives.
In a large bowl, whisk together the flour, baking powder and salt. Set aside.
In a separate large bowl, beat together the butter, sugar and lemon zest until fluffy (about 2-3 minutes). Mix in the oil.
Add in the vanilla extract and beat in the whisked eggs a little at a time.
Turn off the mixer and scrape down the sides of the bowl. Sift in about ⅓ of the dry ingredients. Beat on a low speed until incorporated.
Whisk in about ½ of the milk. I do this by hand.
Then sift in about ⅓ more of the dry ingredients. Beat on a low speed until incorporated. Then whisk in the rest of the milk.
Sift in the rest of the dry ingredients (final ⅓) and beat on a low speed until incorporated. Stop mixing as soon as the dry ingredients are combined.
Gently fold in the fresh lemon juice with a rubber spatula or wooden spoon.
Pour the batter evenly between the 2 pans.
Bake on the same rack in the middle of the oven for 28-32 minutes, or until an inserted toothpick comes out clean.
Cool the cake layers in the pans for at least 20 minutes, then carefully transfer to a wire rack and continue cooling.