Put 5 1/2 cups of raspberries, the sorbet, lime zest, and lime juice into a blender. Use a spatula to push down the ingredients. Pulse a few times, then puree until very smooth. Add ice cream and puree, stopping and stirring with spatula as needed. Stir in 1 cup raspberries.
Pour mixture into glasses. Garnish with remaining 1/2 cup raspberries and lime zest. Serve immediately.