Place the water and sugar into a saucepan and bring to the boil.
Reduce the heat slightly and simmer for 10 minutes until reduced by a third and a light sugar syrup is formed. Remove from the heat and allow to cool.
Peel the lychees, then stone them over the sugar syrup, catching any of the juices. Add the rose water and lime juice and allow to infuse until the liquid is cold. Place in a food blender and process until smooth. Add the egg whites and blitz once more. Pass through a sieve into a bowl.
Pour into an ice cream maker and churn until frozen.
(Alternatively, place in a freezable container and place straight into the freezer, removing to stir several times, breaking up the ice crystals, until frozen.)
Remove and place in a freezable container, in the freezer for 1-2 hours until solid. Remove from the freezer 10 minutes before serving to soften.
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