Preheat your oven to 325°F (165°C). Grease two 9-inch round cake pans with vegetable oil or butter and line the bottoms with parchment paper.

In a large mixing bowl, whisk together the all-purpose flour, cake flour, baking soda, baking powder, and salt until well combined.

In another large bowl, beat together the granulated sugar, vegetable oil, butter-flavored shortening, eggs, vanilla extract, lemon extract, and lemon zest using an electric mixer on medium speed until light and fluffy.

Gradually add the dry flour mixture into the creamed mixture, alternating with the buttermilk. Mix gently until just combined.

Combine the white vinegar with the hot lemon water and stir well. Gently fold this into the batter until incorporated.

Divide the batter evenly between the prepared pans and bake for 25-30 minutes.

Cool in the pans for 10 minutes, then turn out onto wire racks to cool completely.

Beat the softened cream cheese and unsalted butter together until fluffy and smooth. Mix in the lemon juice, lemon zest, and powdered sugar until fully incorporated.

Once the cake layers are cool, spread frosting on top of one layer, place the second layer over it, and frost the top and sides of the entire cake.

Garnish with fresh lemon slices or additional zest for presentation.