Preheat oven to 325° F. In a medium bowl mix together the cake flour, baking powder, and salt. Set aside.
In a small bowl mix together the sour cream, buttermilk, lime juice, lime zest, and vanilla. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat together the sugar and oil for 2-3 minutes, until they’re lighter in color and well-mixed. Add the eggs, one at a time, beating well after each addition.
With the mixer on low speed, add about 1/3 of the flour mixture, followed by ½ of the buttermilk/sour cream mixture. Add another 1/3 of the flour mixture, the last ½ of the buttermilk mixture, and the last 1/3 of the flour mixture. Mix until all ingredients are combined. Be careful not to overmix!
Divide the batter evenly into the three cake pans, pouring over the graham cracker crusts.
Bake for 28-34 minutes, or until a toothpick inserted into the center of the cake comes out clean or with just a couple crumbs stuck to it. Remove from oven and let cool in the pan for 15-20 minutes, then turn out onto a wire rack to cool completely. If making ahead of time, remove the cake layers from the pans and wrap with plastic wrap and store in the freezer for up to 3 weeks.