Prep the pan and oven: Heat oven to 350°F (175°C). Grease and line a 9x13-inch pan or two 8-inch round pans with parchment.
Make the strawberry purée: Blend half the strawberries into a smooth purée.
Finely dice the remaining berries. You’ll need about 3/4 cup purée and 1/2 cup diced strawberries.
Whisk dry ingredients: In a bowl, whisk 1 1/2 cups gluten-free all-purpose flour, 1 cup almond flour, 2 teaspoons baking powder, and 1/2 teaspoon salt.
Cream and combine: In a large bowl, beat 1/2 cup softened butter with 1 cup sugar until light, 2–3 minutes. Mix in 1/4 cup neutral oil, then 3 eggs one at a time.
Stir in 1 1/2 teaspoons vanilla and 1 teaspoon lemon zest.
Add purée and buttermilk: Stir in the strawberry purée. Mix in dry ingredients in two additions, alternating with 1/2 cup buttermilk. Fold in the diced strawberries.
Batter will be thick but spreadable.
Bake: Spread evenly in the pan. Bake 25–35 minutes for 9x13 (or 22–28 minutes for 8-inch rounds), until the top springs back and a toothpick comes out with a few moist crumbs.
Cool completely: Let cool in the pan 15 minutes, then transfer to a rack to cool fully before frosting.
Make the frosting: Beat 8 oz cream cheese and 1/4 cup softened butter until smooth. Add 2–2 1/2 cups powdered sugar, 1 teaspoon vanilla, and 1–2 teaspoons lemon juice.
For extra strawberry flavor, beat in 1–2 tablespoons strawberry jam.
Frost and finish: Spread frosting over the cooled cake. Top with sliced strawberries just before serving.