Prep the pans: Heat oven to 350°F (175°C). Grease and line three 8-inch round cake pans with parchment.
Lightly flour the sides and tap out any excess.
Mix dry ingredients: In a medium bowl, whisk cake flour, baking powder, baking soda, and salt. Set aside.
Infuse the sugar: In a large bowl, rub lemon zest into the sugar with your fingertips until the sugar is fragrant and slightly damp. This step boosts lemon flavor.
Cream the fats: Add butter to the lemon sugar and beat on medium-high until light and fluffy, 2–3 minutes.
Stream in the oil and beat 30 seconds more until creamy.
Add eggs and vanilla: Beat in the eggs one at a time on medium speed, scraping the bowl as needed. Mix in vanilla.
Alternate dry and wet: On low speed, add one-third of the dry mix, then half the buttermilk, another third of the dry, the remaining buttermilk, and finish with the dry. Mix just until combined.
Fold in 1/4 cup of the lemon juice. Do not overmix.
Portion and bake: Divide batter evenly among the pans (a scale helps). Smooth the tops and bake 18–22 minutes, or until the centers spring back and a toothpick comes out clean with a few moist crumbs.
Make the syrup: While cakes bake, simmer 1/4 cup lemon juice and 1/4 cup sugar in a small saucepan until the sugar dissolves.
Cool slightly.
Cool and brush: Let cakes cool in pans 10 minutes, then turn out onto racks. Peel off parchment. While warm, brush tops with lemon syrup.
Cool completely before frosting.
Make the frosting: In a stand mixer, beat cream cheese on medium until smooth, about 30–45 seconds. Add butter and beat until no lumps remain, 1–2 minutes. Gradually add powdered sugar on low.
Mix in lemon juice, vanilla, and salt. Beat on medium until fluffy, about 1 minute. Do not overbeat or it can loosen.
Level and stack: If needed, level cake tops with a serrated knife. Place one layer on a board.
Add about 3/4 cup frosting and spread to the edge. Repeat with second layer. Top with the third layer.
Crumb coat: Spread a thin layer of frosting over the entire cake to trap crumbs.
Chill 15–20 minutes.
Finish frosting: Apply a thicker coat, smoothing the sides and swirling the top. If you like, garnish with thin lemon slices or a sprinkle of zest.
Set and serve: Chill 20–30 minutes to set the frosting for neat slices. Serve at cool room temperature.