Drain the syrup from the can of lychees into a saucepan, add the sugar and heat gently until the sugar has dissolved. Boil for 2 minutes, then take off the heat and leave to cool.
Purée the lychees in a food processor or liquidizer until smooth, or rub through a sieve. Mix with the coconut milk, lime rind and juice. Stir in the sugar syrup when it is cool.
Pour into a shallow plastic container and freeze for 4 hours or until mushy. Beat with a fork or blend in a food processor or liquidizer until smooth. Pour back into the plastic container and freeze for 4 hours or overnight until solid. (Alternatively, freeze in an electric ice-cream machine for 20 minutes, then transfer to a plastic box and freeze until required.)
Allow to soften for 15 minutes at room temperature before serving, then scoop into dishes or chocolate cups (see below) and decorate with kiwifruit wedges and pared lime rind curls, if liked.