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 immersion blender if you like the puree to be smoother. Allow this mixture to reduce to about ½. It will take 20 - 30 minutes. (If you are making this the day before, keep it in the fridge overnight - make sure to remove it an hour before adding it to the batter so it comes to room temperature.)While this is cooking be sure to remove butter, eggs, and sour cream from the fridge. They must be at room temperature for this recipe. When the reduction 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 350 °F (177 °C). If you plan to remove the whole cake from the pan, line the pan with parchment paper and spray it with non-stick spray. If you are planning to leave the cake in the pan, just spray it with non-stick spray. Place your oven rack in the middle of the oven.
In a large bowl, whisk together the flour, baking powder, and baking soda. Set this 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 reduction and sour cream. Do not over beat the mixture.
Add the dry ingredients (flour mixture) and mix only as much as necessary.
Pour this 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. (If you are frosting it in the pan, you do not need to chill it. If you are removing the cake from the pan, it will be easier to frost if it is chilled first.)
Make the strawberry buttercream. Beat the butter until light and creamy. Gradually mix in the icing sugar. Then add the strawberry reduction until the desired consistency is reached.
Notes
If you want tiny pieces of strawberries in your cake and frosting, you can dice up 5 large strawberries and add them to the reduction puree after it's fully cooked, and mix them in. That will just allow you to SEE strawberry pieces and give your cake some texture.
Because this cake has a buttercream frosting, it needs to be refrigerated. Store it covered or in an airtight container for up to 3 days. It can also be frozen for up to 3 months; let it thaw in the refrigerator before serving.