Step 1: Preheat your oven to 350°F (175°C) and grease a 9-inch loaf pan or cake tin with butter.
Step 2: In a large bowl, cream together the softened butter, 1 cup of sugar, and lemon zest until the mixture is light and fluffy.
Step 3: Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next.
Step 4: In a separate bowl, whisk together the flour, baking powder, and salt.
Step 5: Gradually add the dry ingredients to the butter mixture, alternating with the coconut milk. Start and end with the flour mixture.
Step 6: Fold in the shredded coconut gently using a spatula.
Step 7: Pour the batter into the prepared pan and bake for 40-45 minutes, or until a skewer inserted comes out clean.
Step 8: While the cake is baking, combine the 1/3 cup lemon juice and 1/4 cup sugar in a small saucepan over low heat until the sugar dissolves.
Step 9: Once the cake is baked, remove it from the oven and immediately poke holes across the top. Pour the lemon syrup evenly over the hot cake.
Step 10: Allow the cake to cool in the pan for at least 15 minutes before transferring to a wire rack.