Preheat the oven to 175°C. To make the syrup, combine the sugar, water and lemon juice in a small saucepan. Once the mixture comes to a boil, reduce the heat and simmer for 5 minutes. Remove from the heat and set aside to cool.
Grease and flour a round cake tin with a hole in the centre. Sift the flour together with the baking powder, baking soda and salt into a bowl.
In the bowl of a stand mixer, beat the butter and sugar until light and fluffy, about 2 minutes. Add the eggs one at a time, beating well after each addition. Add the vanilla and mix to combine.
Add 3 tablespoons of the flour mixture and beat until incorporated. Add the milk and the remaining flour mixture. Beat just until combined, being careful not to overmix. Finally, add the coconut and gently fold it in with a spatula.
Pour the batter into the prepared cake tin and bake for 45 minutes.
Remove the cake from the oven and let it stand for 5 minutes. Then carefully invert it onto a serving platter. Using a pastry brush, generously brush the syrup all over the cake. It may seem like a lot of syrup, but don't worry—the cake will absorb it all.
Sprinkle with extra coconut and allow the cake to cool completely, for at least 2 hours, before slicing and serving.