1. Preheat oven to moderate (350° F.). Grease two nine-inch layer cake pans, line with waxed paper and grease the paper.
2. Into the bowl of an electric mixer sift the flour, sugar, baking powder and salt. Add the shortening, three-quarters cup of the coconut milk and the vanilla. Beat two minutes at low to medium speed, scraping the bowl and beaters as necessary.
3. Add the egg whites and the remaining coconut milk and beat two minutes longer.
4. Turn the batter into the prepared pans and bake until a cake tester inserted in the center of the cake comes out clean, about twenty to thirty minutes.
5. Cool the cake on a rack ten minutes before removing from the pans.
6. When the cake is completely cool, spread a lemon filling (prepared from a packaged mix) between the layers. Frost with vanilla boiled frosting or with sweetened whipped cream. Sprinkle with freshly grated coconut