Preheat oven to 350°F (177°C). Grease three 8-inch round cake pans with solid vegetable shortening or Wilton cake release, line with parchment paper rounds, then grease the parchment paper.
For the cake
In the bowl of your stand mixer, beat the butter on high until smooth and creamy, about 1 minute. Add granulated sugar and beat on medium speed until combined, about 2 minutes. Add the oil and beat until combined and light and creamy, about three more minutes. Add the eggs and vanilla, and beat on medium speed until everything is thoroughly combined, about 1 minute. Stop the mixer and scrape down the sides and bottom of the bowl.
In another large bowl, whisk together the flour, baking powder, baking soda, and salt. Add the dry (flour) ingredients to the wet ingredients. Beat on low speed for a few seconds, then add the milk, lemon zest, and lemon juice until just combined.
Toss the blueberries with one tablespoon of flour and gently fold them into the batter. Don't overmix.
Spoon batter evenly into prepared cake pans. (I weigh the layers to get them even.)
Bake for 22–26 minutes or until a toothpick inserted in the center comes out clean. Remove from the oven and allow to cool for 10 minutes in the pan before turning them out on a wire rack to cool completely.
Make the frosting: Using a handheld or stand mixer with a paddle attachment, beat cream cheese and butter together on medium speed until no lumps remain, about 3 full minutes. Add confectioners’ sugar, heavy cream, vanilla extract, and salt with the mixer running on low. Turn mixer up to high speed and beat for 3 minutes.
Assemble and frost
Cool cake layers are easier to handle and frost. You can make these layers a day ahead, wrap them in plastic wrap, and refrigerate.
Cream the butter and cream cheese together until smooth and fluffy. With the mixer on low, slowly add the powdered sugar, heavy cream, vanilla, and salt. Stop the mixer and scrape the sides. Beat until smooth and fluffy. From here you have two options.
For the frostingOption 1: You have a couple of options for the frosting. You can make the above-listed cream cheese frosting (do not stir in the Cool Whip) and frost the entire cake with it. It's classic cream cheese frosting that most everyone loves, and it pairs beautifully with this cake. Option 2: Make the above-listed cream cheese frosting. Take half of the frosting and spread it between the cake layers. To the remaining half of the frosting, fold in the 6 ounces of Cool Whip. Frost the sides and top of the cake.
How to frost a layer cake: When you are ready to frost the cake, the first step is to make the tops of each cake flat if it isn't already. Using a large serrated knife, slice a thin layer off the tops of the cakes to create a flat surface. Place 1 layer on your cake stand. Evenly cover the top with cream cheese frosting. Top with 2nd layer, more frosting, then the third layer. Top with frosting and spread around the sides.
Garnish with blueberries and lemon slices, if desired.
Refrigerate for at least 1 hour before cutting to let it set. Otherwise, it may fall apart as you cut.
Cover leftover cake tightly and store in the refrigerator for up to 5 days.