The first step is to make the strawberry puree. Remove the stems of the strawberries. Place them into a medium pot. Add the sugar and lemon juice.
Heat this at medium heat, stirring often to avoid boiling. Once this mixture begins to boil, you may turn the heat down to medium low. Stir often and the strawberries will continue to break down. Use an emulsion blender if you like the puree to be smoother.
Allow this mixture to reduce to about half. It will take 20-30 minutes. When the puree is finished, remove it from the heat and allow it to come to room temperature before adding it to the recipe.
Preheat the oven to 350F degrees. Spray a 9x13-inch pan with non-stick spray (I like the kind with your in it, like Baker's Joy). Place your oven rack in the middle of the oven.
In a large bowl, whisk together the flour, baking powder, and baking soda, set aside.
Using a stand or handheld mixer, beat the butter until it is smooth and creamy.
Blend in the oil, then gradually add in the sugar and beat until smooth.
Mix in the vanilla extract and then add the eggs one at a time, mixing between each one.
Then gradually mix in the strawberry puree and sour cream.
Add the dry ingredients (flour mixture). Do not overmix. Mix until you no longer see any white bits.
Pour batter into the prepared pan.
Bake the cake for 25-30 minutes or until a toothpick inserted comes out clean. Remove it to a cooling rack and allow it to cool completely before frosting.
Make the strawberry buttercream: beat the butter until light and creamy. Gradually mix in the powdered sugar.
Then add the strawberry puree until the desired consistency is reached.
Spread frosting all over the cake. Slice and serve.
Notes
You can make this in different sized pans, see tips above.
The reduction can be made the day before and kept in the refrigerator to make sure it cools completely.
The cake can be frozen, see above on how to do that.
Use fresh or frozen strawberries, make sure the strawberries are thawed.