Partially freeze steak; trim fat from steak. Slice steak diagonally across grain into 1/4-inch-wide strips.
Combine rum and next 7 ingredients in a small bowl; stir well, and set aside.
Coat a wok with cooking spray; drizzle oil around top of wok, coating sides. Heat at medium-high (375°) for 2 minutes or until hot. Add steak, and stir-fry 5 minutes or until browned. Remove from wok; drain well on paper towels, and set aside. Wipe wok dry with a paper towel.
Coat wok with cooking spray. Add green pepper and green onions; stir-fry 3 minutes. Add steak, rum mixture, mango, and carambola; stir-fry 1 to 2 minutes or until mixture is slightly thickened.
Arrange 1 cup lettuce on each of 4 individual serving plates. Spoon 1 cup steak mixture in center of each serving.