Season flank steak with salt and pepper and 1/4 cup lime juice. Heat oil in a 12-inch non-stick skillet over medium high heat. Add flank steak and cook to medium rare, turning once, about 6 to 7 minutes per side. Remove to a cutting board and let rest.
In a large, non-reactive salad bowl, whisk together remaining lime juice, fish sauce, sugar, chili paste and cilantro. Add cucumber, mango and lettuce leaves to dressing. Toss until combined. Divide among 5 serving dishes.
Slice flank steak very thin and divide slices among the salads. Place over greens.
If using reserved cooked steak, there is no need to cook it again. Just slice it thinly and use.