Make the sugar syrup: In a medium saucepan, combine the sugar with 1½ cups water. Cook over moderate heat, stirring, until the syrup is clear and the sugar is dissolved. Remove from the heat and cool completely.
Peel and seed the melon; cut into large cubes. Puree in a food processor, then strain through a sieve into a bowl. Stir in the sugar syrup. Add enough lem