In the bowl of a stand mixer fitted with a paddle attachment, mix the dry ingredients together.
Add the room temperature butter and oil then beat until the mixture is well combined and starts clumping together. You want the butter to be dispersed with no lumps remaining in the flour.
Whisk the eggs, coconut milk, lemon juice and zest together.
Pour the wet ingredients into the batter while mixing on a low speed. Beat until just combined.
Pour the batter into a greased and lined loaf pan (the one I used was 9"x 5" or 22cm x 12cm).
Place in the oven and bake for 45-60 minutes or golden brown and a skewer inserted comes out clean.
Remove from the oven and allow to cool for 20 minutes in the pan before turning out and cooling completely.
Whisk the lemon juice, coconut milk and icing sugar together then drizzle over the cake.
Decorate with strawberries and coconut flakes (optional) and serve.