Preheat the oven to 350 degrees Fahrenheit. Lightly spray 3 8-inch cake pans with non-stick baking spray. Set aside.
In medium bowl, measure out the flour, baking powder, baking soda, and salt. Add in the zest of 2 lemons and mix. Set aside.
In a stand mixer, beat the butter, oil and sugar together for 3-5 minutes or until light and fluffy. Add in one egg at a time, being sure to scrape the mixing bowl down after each addition. Beat on high speed for one minute. Once the eggs are fully incorporated add in the lemon juice and vanilla.
With the mixer on low, add in the dry ingredients, then add in the wet ingredients. Mix until fully combined being sure not to overmix.
Separate the batter evenly into the 3 cake pans. Bake for 18-21 minutes or until a toothpick comes out clean.
In a heavy bottomed saucepan, add in the raspberries, water and sugar. Allow to boil over medium heat until the raspberries break down into a puree like consistency, this should take about 10-15 minutes. Let it cool before using.
In a stand mixer, mix the butter and powdered sugar together. Add in the milk, 1 tablespoon at a time, adding more if too stiff.
Mix on medium speed for 5-8 minutes or until light and fluffy. Add in 3 tablespoons of raspberry puree and mix on medium speed for an additional 3 minutes.
Frost the cake with the icing, or store in an airtight container in the fridge until ready to use.