1. Soak wooden skewers in hot water 30 minutes. Toss banana slices with lemon juice.
2. Thread banana slices, pineapple, and star fruit alternately onto skewers. Place on a wire rack in an aluminum foil-lined broiler pan. Cover and chill up to 8 hours, if desired.
3. Preheat oven to broil. Combine sugar and cinnamon; sprinkle over fruit.
4. Broil 4 inches from heat 5 minutes on each side or until lightly browned. Drizzle with rum.