Combine sugar and water in a small saucepan. Bring to a boil; cook 1 minute or until sugar dissolves. Cool completely.
Place cantaloupe and watermelon in a blender or food processor, and process until smooth.
Combine the sugar syrup, melon mixture, and lime juice.
Pour the sorbet mixture into the freezer can of an ice-cream freezer, and freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze 1 hour or until firm.
