Heat water and sugar in a saucepan over medium-high heat until sugar has dissolved, stirring occasionally. Allow to cool.
Place watermelon in a blender or food processor. Blend until smooth.
Whisk watermelon, lime juice and syrup together in a large bowl. Cover and chill in the refrigerator.
Pour the chilled mixture into an ice cream maker and freeze according to manufacturer's directions until it reaches "soft-serve" consistency.
Transfer sorbet to a one- or two-quart lidded plastic container; cover surface with plastic wrap and seal. For best results, sorbet should ripen in the freezer for at least 2 hours or overnight.
