Preheat oven to 350 degrees F. Brush a doughnut pan with coconut oil.
To make the doughnuts, combine the almond flour and baking soda in a large bowl with the cinnamon and nutmeg.
Whisk the maple syrup, coconut oil, and lemon juice with the egg yolks and add it to the flour. Mix until just combined.
Beat the egg whites until firm peaks form and carefully fold this mixture into the batter.
Line a large measuring cup or tall bowl with a gallon size freezer bag. Transfer the batter to the bag and cut off the tip. Pipe the batter into the doughnut molds and bake for 12-15 minutes.
While the doughnuts are baking, remove the coconut milk from the refrigerator without shaking. Open and take the cream out of the top of the can, reserving the milk for another use. Put the cream in a bowl with the vanilla and maple syrup and whisk until you have a thick glaze.
Cool the doughnuts completely before glazing with the frosting. Sprinkle with the walnuts.