Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans, line bottoms with parchment, and set aside.
Sift together all-purpose flour, cake flour, baking soda, baking powder, and salt into a large bowl. Whisk to combine thoroughly.
In a stand mixer with paddle attachment, beat vegetable oil and shortening on high for 2 minutes. Add sugar and beat 3-4 minutes until pale and fluffy.
Add eggs one at a time, beating well after each addition and scraping down the bowl. Add vanilla and lemon extracts, beat 30 seconds. Fold in lemon zest and juice.
On low speed, alternate adding dry ingredients in three additions with buttermilk in two additions, beginning and ending with dry ingredients. Mix until just combined—do not overmix.
Divide batter evenly between prepared pans, smooth tops, and bake 28-33 minutes until tops spring back and toothpick comes out clean.
Cool in pans on wire rack for 10 minutes, then run a knife around edges, invert onto rack, peel off parchment, and cool completely to room temperature.
Beat softened cream cheese in stand mixer with paddle on medium for 2 minutes until smooth. Add butter and beat 2-3 minutes more until combined.
Reduce speed and gradually add sifted powdered sugar in two additions. Add lemon juice, lemon extract, lemon zest, and salt. Beat on medium-high 1-2 minutes until fluffy.
Level cake layers if domed. Place one layer on serving plate, spread with frosting, top with second layer. Apply thin crumb coat, chill 20-30 minutes, then finish with final frosting layer.