Position a rack in the middle of the oven and preheat the oven to 350 F (175 C). Butter three 9-by-2 inch (23 by 5 cm) round cake pans, then line the bottoms with parchment and butter it as well. Lightly dust the pans with flour, tapping the pans on the counter to shake out the excess.
Sift together the flour, baking soda, and salt into a medium bowl. Set aside
In a large measuring cup or small bowl, combine the buttermilk and vanilla. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment (or in a large mixing bowl, using a handheld mixer) cream the butter, coconut oil, and sugar together on medium-high speed until light and fluffy, 3 to 5 minutes. Add the egg yolks one (19 g) at a time, beating well after each addition and scraping down the sides and bottom of the bowl with a rubber spatula as necessary. Then continue to beat until light in color and texture, 2 to 3 minutes.
Turn the mixer speed down to low and add the flour mixture in thirds, alternating with the buttermilk mixture and beginning and ending with the flour, mixing until just combined. Gradually add the 1 cup (80 g) coconut. If using a stand mixer, transfer the batter to another large bowl (if you don't have a second mixer bowl).
Wash and dry the mixer bowl and wipe the inside of the bowl (or another large mixing bowl) with the lemon juice to make sure the bowl is squeaky clean. Attach the bowl to the mixer stander (if using) and fit it with a whisk attachment. Put the egg whites in the mixer bowl (or large mixing bowl) and beat (with clean beaters if using a handheld mixer) until stiff peaks form, 3 to 5 minutes.
Scoop up a little of the egg whites with a rubber spatula and gently stir them into the cake batter to lighten it and make it easier to fold in the rest of the egg whites. Then gently fold in the remaining egg whites until thoroughly incorporated, about 1 minute.
Gently scrape the batter into the prepared pans, dividing it evenly. Smooth the tops with a spatula.
Bake for 20 to 25 minutes, until a cake tester inserted in the center of a cake comes out clean and the cake is light golden. Let the cakes cool in the pans on a large wire rack for 20 minutes then invert them onto another rack, peel off the parchment and let cool completely.