Add strawberries, lemon juice, and sugar (if using) to a blender. Blend smooth.
Pour puree into a small saucepan. Simmer over medium heat, stirring often, until reduced by about half and thick like a loose jam, 10–15 minutes. You should have roughly 3/4 to 1 cup.
Cool completely. Thick puree equals stronger flavor and better texture.
Heat oven to 350°F (175°C). Grease and line two 8-inch round cake pans with parchment. Lightly flour the sides.
Whisk flour, baking powder, baking soda, and salt in a bowl.
In a large bowl, beat butter, oil, and sugar until pale and fluffy, about 2–3 minutes.
Beat in eggs one at a time, scraping the bowl as needed, then add vanilla.
Mix in sour cream until smooth.
Stir strawberry puree and jam together. The jam boosts berry depth.
Add dry ingredients to the wet in two additions, alternating with the strawberry mixture. Start and end with dry. Mix just until combined; do not overmix.
Divide batter evenly between pans. Tap pans on the counter to release big air bubbles.
Bake 24–28 minutes, until the centers spring back and a toothpick comes out with a few moist crumbs.
Cool in pans 10 minutes, then turn out onto a rack. Peel off parchment and cool completely.
Beat cream cheese and butter until smooth and fluffy.
Mix in 3 1/2 cups powdered sugar, vanilla, salt, and strawberry puree or powder. If using puree, add it slowly so the frosting stays thick.
Adjust with more powdered sugar for a pipeable consistency.
Level cake layers if needed. Place the first layer on a plate.
Spread a generous layer of frosting. Top with the second cake.
Apply a thin crumb coat, chill 15 minutes, then finish with a thicker layer. Swirl the top and decorate with sliced strawberries if serving soon.
Tip: For extra strawberry punch, spread a thin layer of strawberry jam over the first layer before frosting.
Make it a sheet cake: Bake in a 9x13-inch pan for 30–35 minutes. Frost the top and slice into squares.
