Place the flour in a large bowl, add the yeast to one side and the sugar and salt to the other. Add the coconut milk and lemon zest and stir to form a dough, adding a splash of water as needed until all of the flour has been picked up.
Turn out on to an un-floured surface and knead for about 10 minutes until smooth and elastic (use a stand mixer if you have one), the dough should be sticky at first but will become smooth after a few minutes of kneading.
Add the softened butter and knead until it is fully combined and the dough is smooth and stretchy. It should still have a fairly soft, sticky texture, resist the urge to add more flour.
Transfer the dough to a lightly greased bowl, cover and place in a warm spot for an hour or so until doubled in size.
Line a 2 lb loaf tin with greaseproof paper. For the filling, place the sugar and lemon zest in a bowl, use your fingertips to rub them together to release the oils from the lemon, then stir in the desiccated coconut.
Roll the dough out on a lightly floured surface into an approx 30 x 45cm (12 x 18 in) rectangle. Use your hands to spread the butter evenly over the dough. Scatter over the coconut sugar mixture and press it down gently.
Slice the dough widthways into 5 even strips (a pizza cutter is the ideal tool), then lengthwise into 4 strips, to make 20 squares of dough. Stack the squares into 5 piles, each with 4 squares.
Stack the dough piles upright in the tin, squashing them together to fit them all in. Gather up any coconut filling that fell off and scatter it over the top. Loosely cover the tin, and leave to rise in a warm place for about 45 minutes until puffy.
Meanwhile, preheat the oven to 190°C/170℃ fan/375°F/gas mark 5.
Bake for about 45 minutes until the temperature in the centre registers at least 90°C/194°F on a probe thermometer, or a skewer inserted into the centre comes out clean.
Allow to cool for 10 minutes in the tin on a wire rack.
Meanwhile, make the glaze; sift the icing sugar into a small bowl and stir in the coconut milk and lemon juice. It should be a pourable consistency, add a little more lemon juice if it is too thick or a little more icing sugar if it is too thin.
Turn the bread out onto a serving dish and pour over the glaze. Serve warm.