Preheat the oven to 325°F. Lightly grease two 6 by 3-inch cake pans with palm shortening and place a round piece of parchment paper at the bottom of each pan.
In the bowl of a stand mixer fitted with the whisk attachment, or using an electric handheld mixer, beat the egg whites on medium-high speed for 3 to 5 minutes, until they have tripled in volume and form soft peaks when the whisk is pulled out. Scoop the whites into a bowl and set aside. Return the bowl to the mixer and switch to the beater attachment. Beat together the coconut milk, palm shortening, honey, maple syrup, vanilla, and lemon juice on medium-high speed for 30 seconds. Add the almond flour, arrowroot, coconut flour, and baking soda and beat again for 30 seconds, or until well incorporated. Gently fold in the beaten egg whites with a rubber spatula until they are fully incorporated and there are no visible ribbons of whites throughout the batter. Divide the batter between the two pans.
Bake the cake for 30 minutes, or until a toothpick inserted into the center of the cakes comes out clean.
Cool the cakes on a wire rack for 1 hour, then use a knife to gently release the cakes from the sides of the pans. Flip the pans over to release the cakes and cool completely right side up before frosting.
Make it ahead: The cake can be made up to 3 days in advance. Wrap the layers in parchment paper first, then tightly with plastic wrap and store in the refrigerator. Bring to room temperature before frosting.
Tidbits: The color of the honey used will dictate the color of this cake. I suggest using a light-colored, mild-flavored raw honey, such as clover.