Preheat the oven to 350° F (180° C) and grease a loaf pan (or any other baking dish) or line it with parchment paper.
If not ground already, start by grinding oats into flour.
To a bowl add oat flour and all the other dry ingredients, thus sugar, lemon zest, baking powder, vanilla (if using powder) and salt. Mix well to combine.
In another bowl mix together all the wet ingredients (apple sauce, milk water and lemon juice) and add to dry ingredients.
Pour batter into loaf pan and bake for 40-45 minutes or until a toothpick inserted comes out (mostly) clean. But be sure to check on the cake regularly starting about 35 minutes onwards.
Transfer the cake to an oven rack or something similar and let cool.
In the meantime prepare the icing by melting coconut butter (if solid) in a double boiler. Add maple syrup and lemon juice and ice the cake.
Let cool completely before serving.