Stir together marinade ingredients and reserve one fourth of marinade for sauce.
Put steak and remaining three fourths of marinade in a glass dish, turning steak to coat, and marinate at room temperature, turning once, 30 minutes. While steak is marinating, cut apples and mango into 1- by 1/4-inch sticks. Toss together with juice and chili sauce and season with salt.
Preheat broiler.
Broil steak on rack of a broiler pan 2 to 3 inches from heat until slightly charred, 2 to 3 minutes on each side for medium meat. Let steak stand 5 minutes. Cut crosswise into 1/4-inch-thick slices, then halve slices crosswise. Toss beef in reserved marinade with salt and pepper to taste and divide among lettuce leaves. Top with fruit and sesame seeds.
