Preheat your oven to 335º F/168º C Prepare three, 6"x2" or two, 8"x2" cake pans with cake goop or another pan release. For square pans or cakes over 12", I also use parchment paper.
Combine the 4oz of buttermilk with the oil and set aside.
To the remaining 6oz of buttermilk, add your eggs, lemon zest, lemon extract, and lemon juice. Whisk lightly to break up the eggs and set aside.
Place cake flour, sugar, salt, baking powder, and baking soda into the bowl of your stand mixer with the paddle attachment attached.
Turn the mixer onto the lowest speed. Add in your softened butter in small chunks mix until the flour mixture resembles coarse sand.
Add your oil/milk mixture all at once to the dry ingredients and mix on medium (speed 2 on a bosch, speed 4 on KitchenAid) for 2 full minutes to develop the cake's structure.
Scrape the bowl. This is an important step. If you skip it, you will have hard lumps of flour and unmixed ingredients in your batter. If you do it later, they will not mix in fully.
Slowly add in the milk/egg mixture in 3 parts, letting the batter mix for 10 seconds between additions. Stop to scrape the bowl once more halfway through. Your batter should be thick and not separated. If it is separated, some of your ingredients could have been too cold or you added your liquids too quickly.
Fill your cake pans 3/4 full with cake batter. Give the pan a little tap on each side to level out the batter and get rid of any air bubbles. You can also weigh your cake pans to ensure that each pan has the same amount of cake batter.
Bake at 335º F/168º C for 35-40 minutes or until a toothpick comes out cleanly from the center of the cake and the top of the cake bounces back when you touch it.
After cakes have cooled for 15 minutes or the pans are cool enough to touch, flip the cakes over onto a cooling rack and let cool until barely warm. Wrap your cakes in plastic wrap and chill in the refrigerator before frosting so they are easier to handle. You can also put them in the freezer if you are in a hurry for them to cool down.
Once the cakes are chilled you can now trim, fill, and decorate your cake as you wish.