Place parchment-paper circles in the bottoms of three 8-inch round cake pans. Grease the sides thoroughly to help the baked layers release cleanly.
Preheat the oven to 350°F (176°C).
Add the all-purpose flour, baking powder, baking soda, and salt to a medium bowl. Stir until the leavening ingredients and salt are evenly dispersed, then set the mixture aside.
Place the softened butter, neutral oil, granulated sugar, and vanilla extract in a large mixing bowl. Beat at medium speed for 1½–2 minutes, or until the mixture appears pale and fluffy.
Incorporate the eggs individually, mixing only until each egg is blended before adding the next. Scrape the sides and bottom of the bowl whenever necessary.
Add half of the prepared flour mixture to the creamed ingredients. Mix briefly, stopping when the dry ingredients are mostly incorporated.
Pour in the milk and freshly squeezed lemon juice, then add the grated lemon zest. Mix until the liquids and zest are evenly distributed throughout the batter.
Add the remaining flour mixture and blend just until the batter becomes smooth. Avoid excessive mixing, which may produce a less tender cake. Scrape the bowl as needed to ensure uniform consistency.
Distribute the batter evenly among the three prepared pans.
Bake for 22–25 minutes. The layers are ready when a toothpick inserted into the center emerges with only a few moist crumbs attached.
Leave the cakes in their pans for 2–3 minutes after removing them from the oven. Carefully turn the layers onto wire racks and allow them to cool completely before assembly.
To prepare the frosting, beat the softened cream cheese and butter together in a large mixer bowl until completely smooth and evenly combined.
Add approximately half of the sifted confectioners’ sugar. Mix until the sugar is fully incorporated and the frosting is smooth.
Blend in the fresh lemon juice and grated lemon zest.
Add the remaining confectioners’ sugar and continue beating until the frosting is light, fluffy, and easy to spread.
Once the cake layers are fully cooled, trim their domed tops with a large serrated knife when leveling is necessary.
Position the first cake layer on a serving platter or cake board. Spread approximately 1 cup of lemon cream cheese frosting evenly across its surface.
Set the second layer over the frosting and cover it with another 1 cup of frosting.
Add the final cake layer. Apply the remaining frosting over the top and around the sides, smoothing the surface evenly.
Decorate the top with piped frosting swirls and lemon slices, when desired.