Melt the sugar with a spoonful of water in a saucepan until golden, and pour into an 8-inch/20 cm metal cake tin. It will harden in about five minutes.
Meanwhile, whisk together all the remaining ingredients except for the lime zest and coconut. Strain the custard over the hardened caramel. Scatter over the lime zest and coconut and swirl a bit with a spoon to blend evenly.