Preheat the oven to 350. Prepare two 8-inch cake pans by greasing the sides and coating with a thin layer of flour, tapping the excess off, and discarding it. Line the bottom of the cake pans with parchment paper.
In a large bowl, combine 2 1/2 cups flour, 1 tsp baking soda, 1 tsp baking powder, and 1 tsp salt. Stir to combine completely.
In the bowl of a stand mixer, fitted with the whisk attachment, add 1 1/2 cups sugar, 1 cup sour cream, 1/2 cup vegetable oil, and 1/4 cup softened butter. Whisk until well combined.
Add 3 eggs, one at a time, whisking in between additions.
Add the 2 Tbsp key lime juice, 1 Tbsp lemon juice, 1/w Tbsp lime zest, and 1 tsp vanilla. Whisk until combined.
Switch to the paddle attachment. Add flour, a cup at a time, and beat until completely combined. Start slowly until the mixture begins to become one, and then beat on medium-high until just combined.
Divide the batter among the two prepared pans. Bake for 27-32 minutes, or until the cake springs back when pressed lightly or a toothpick comes out clean.
Allow cakes to cool in the pan for 15 minutes, and then transfer them to a wire cooling rack.