Finely shred 2 teaspoons peel from lime. Juice lime (2 tablespoons); set aside.
In a medium saucepan stir the sugar and water over medium heat until just simmering, stirring to dissolve sugar. Remove from heat. Add raspberries and lime juice. Stir to thaw.
Place raspberry mixture and watermelon in a food processor or blender. Cover and process or blend until smooth. Press mixture through a fine-mesh sieve; discard seeds. Stir in lime peel.
Transfer mixture to a 2-quart rectangular baking dish. Cover; freeze until firm (4 to 24 hours). Transfer to a chilled bowl, breaking up if necessary. Beat with an electric mixer on low to medium speed until smooth and lightened in color. Return to dish. Cover and freeze for 2 to 4 hours or until firm.