Preheat the oven to 350 degrees F (175 degrees C). Lightly grease two 9-inch cake pans and sprinkle with flour if pans don’t have a smooth bottom.
Whisk 3 cups flour, cocoa powder, baking soda, and salt together in a bowl.
Beat 1/2 cup butter in a bowl using an electric mixer until creamy and smooth. Add 1 1/2 cups sugar and beat until fairly creamy, about 2 minutes. Pour in vegetable oil and beat until combined, about 30 seconds more.
Beat in egg yolks, vanilla extract, vinegar, and enough food coloring to reach desired color. Pour in flour mixture, alternating with buttermilk, on low speed until just incorporated, making sure to not overmix the batter.
Beat egg whites until thick and frothy in a separate bowl; fold into the batter. Pour batter into the prepared cake pans.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 30 to 35 minutes. Be careful not to overbake. Let cakes cool in the pans for 10 to 20 minutes before transferring to a wire rack or serving plate to cool completely.
Whisk sugar, flour, and salt in a saucepan to combine. Whisk in milk gradually, making sure there are no lumps. Place saucepan over medium heat. Stir until thickened. Pour mixture into an airtight container and refrigerate until completely cool, about 1 hour.
Place frosting in a mixing bowl. Add lemon juice and vanilla extract. Mix with an electric mixer on high speed to combine. Whip in cream cheese, 1 tablespoon at a time. Whip in butter and continue to mix until you have a really thick frosting. Place into an airtight container and refrigerate if not using immediately.
Frost cooled cake and place sliced strawberries between the 2 layers.
Per Serving: 820 calories; 49.3 g fat; 85.9 g carbohydrates; 10.2 g protein; 143 mg cholesterol; 479 mg sodium.