Bring sugar and water to a boil in a small saucepan, stirring until sugar has dissolved. Remove from heat and add lavender. Let steep 10 minutes. Pour through a fine sieve set over a bowl; discard solids. Refrigerate syrup until cold, about 15 minutes.
Puree grapes in a blender until smooth. Pour through a fine sieve set over a bowl; discard solids. Stir in lavender syrup, cover, and refrigerate until cold, at least 1 hour and up to 2 hours.
Chill a loaf pan in freezer at least 10 minutes. Freeze and churn grape mixture in an ice cream maker according to manufacturer's directions, then transfer to pan. Cover with plastic wrap and freeze until hardened, at least 2 hours; sorbet can be frozen up to 2 weeks ahead.