Preheat the oven to 325 degrees F. Spray three 8-inch round cake pans with nonstick spray. Line the bottom of each pan with parchment paper, then spray the pans again.
Combine the flour, baking powder, lime zest, and salt into a medium mixing bowl and whisk to combine. Set aside.
In the bowl of an electric mixer, combine the butter and the sugar. Beat until light and fluffy, about 3 to 5 minutes.
Gradually add the egg whites, making sure to mix well between each addition, being sure to scrape down the sides and bottom of the bowl as you go along. Once all of the egg whites are added, mix for an additional 3 minutes, until the mixture is lighter in color and smooth in texture. You'll also notice the volume increases.
While the butter, sugar, and eggs mix, stir together the buttermilk and lime juice.
Turn the mixer to low speed. Alternately add the flour mixture and the buttermilk mixture, starting and ending with the flour mixture. Stir just until combined.
Divide the pans evenly between the three cake pans, about 16 ounces in each pan. Bake the layers for 25 to 30 minutes, or until a toothpick inserted in the center of the cake comes out with a few moist crumbs on it.
Allow layers to cool in the pans for about 15 minutes before inverting them onto cooling racks to cool completely. Wrap in plastic wrap and chill until ready to use. If you need to level the cake layers, be sure to do that BEFORE you freeze them.