Heat the sugar gently in a saucepan with water until dissolved, then bring to the boil and simmer for 1 minute. Set aside to cool, then stir in the lime juice.
In a blender, whizz the lime syrup with the watermelon until very smooth. Add the rum, to taste, but go carefully and don't add to much rum as this will prevent the lollies from freezing.
Sieve the mixture to make sure you don't have any seeds or lumps in the mixture.
Divide the mixture between 8 lolly moulds and freeze them until fully frozen. 2 hours at least
To serve, run the moulds under warm water for a few seconds until easy to release.