Soak wooden skewers 30 minutes to prevent burning.
Toss banana slices with lemon juice.
Thread banana slices, pineapple, and star fruit onto skewers, alternating fruit. Place on an aluminum foil-lined broiling rack. Cover and chill up to 8 hours, if desired.
Combine sugar and cinnamon; sprinkle evenly over fruit.
Broil, in 2 batches, 4 inches from heat 5 minutes on each side or until lightly browned. Drizzle with rum.
*4 papayas, peeled and cut into 1/2-inch pieces, may be substituted for star fruit.