For sorbet, in a medium saucepan combine granulated sugar and the water. Bring to boiling, stirring until sugar dissolves. Stir in lemon peel, lemon juice, and limoncello. Cover and chill for at least 4 hours.
Transfer lemon mixture to a 2- to 4-quart ice cream freezer. Freeze according to the manufacturer's directions. Transfer sorbet to a nonmetallic freezer container with a tight-fitting lid. Cover and freeze for 8 to 24 hours or until firm.
Place powdered sugar in a small bowl. Dip strawberries into powdered sugar, turning to coat. Place strawberries on a greased grill tray.
For a charcoal grill, grill strawberries on grill tray on the rack of an uncovered grill directly over medium-low coals about 6 minutes or until strawberries are heated through, turning frequently. (For a gas grill, preheat grill. Reduce heat to medium-low. Place strawberries on grill tray on grill rack over heat. Cover and grill as directed.)
Halve strawberries. If desired, thread strawberry halves onto 4-inch skewers. Serve with sorbet.