Mix together the flours, oats, and baking soda; set aside.
With and electric mixer, beat coconut oil and sugar for 1 minute, add eggs, milk, vanilla and lemon peel; beat well. Stir in zucchini. Add flour mixture, a third at a time beating on low speed just until combined. Stir in nuts.
To bake the cake, I used really large muffin papers. They don’t fit into a regular muffin pan, so I used small bowls to put the papers in. These get baked for 35-40minutes at 350°F.
Otherwise grease a loaf pan and bake 50-60 minutes at 350°F
If cake is getting too brown on top, cover with foil for the last 10 minutes.
Stir the icing sugar and rum together until smooth and lump free.
Drizzle icing on top of cooled cake.