Combine 2 cups sugar and water in a large heavy saucepan. Bring to a boil; cook 1 minute or until sugar dissolves. Add 1 1/2 cups lemon juice; stir well. Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sorbet into a freezer-safe container; cover and freeze lemon sorbet 8 hours or until firm.
Place 1 1/4 cups sugar in a Dutch oven. Place over medium heat; cook until sugar is golden (do not stir). Carefully add cranberry juice and 1/2 cup lemon juice, stirring constantly (mixture will bubble vigorously); cook 35 minutes or until reduced to 2 1/4 cups. Cover and chill.
Prepare grill. Thread 3 strawberries onto each of 16 (6-inch) skewers. Dredge skewers in powdered sugar. Place skewers on grill rack coated with cooking spray; grill 2 minutes on each side or until thoroughly heated. Serve with sorbet and syrup.