In a large saucepan, bring water and sugar to a boil over medium-high heat. Cood for 5 minutes, stirring constantly. Remove from heat and allow to cool to room temperature, about 30 minutes.
Meanwhile , peel and seed melon. Cube, then puree in a food processor. Stir in cooled syrup mixture and lemon juice. Pour mixture into an ice cream maker and freeze according to manufacturer's directions.