Preheat oven to 350 degrees F. In a large mixing bowl, combine butter, oil, and sugar. Whisk together for 1-2 minutes, then add eggs. Continue to whisk until eggs are fully incorporated and then add sour cream, milk, vanilla extract, lemon extract, lemon zest, and lemon juice. Whisk all ingredients together until a smooth batter forms.
In a separate bowl, combine flour, baking powder, baking soda, and salt. Whisk together and add to the wet ingredients. Fold into the wet ingredients until just combined.
Spray a 12-cup muffin pan with oil. Add cupcake liners and fill each cup ¾. Bake for 20-22 minutes, until a toothpick comes out clean.
While cupcakes are baking, make the raspberry buttercream. In the bowl of a stand mixer with the paddle attachment, add room temperature butter and beat butter on medium speed for 3 minutes. Add raspberries and continue to beat together for another minutes.
Scrape down the sides of the bowl and add 1 cup of powdered sugar, continuing to mix on medium speed for 1 minutes, then increasing the speed to high for about 10 seconds. Reduce speed back to medium and add powdered sugar. Repeat until all powdered sugar is added.
Continue to mix on medium speed and slowly add heavy cream, one tablespoon at a time. If using, add raspberry extract. Place in the refrigerator until lemon cupcakes are fully cooled and ready to be iced.
Pipe/ice each lemon cupcake with raspberry icing.