Prepare grill to medium-high heat.
Sprinkle the steak with salt and black pepper. Place steak on a grill rack coated with cooking spray, and grill 4 minutes on each side or until desired degree of doneness. Let rest 5 minutes.
Cut steak diagonally across grain into thin slices. Combine sliced steak, cucumber, and next 5 ingredients (through cilantro) in a large bowl. Combine sugar, soy sauce, juice, and red pepper. Drizzle over steak mixture; toss well to coat.
Warm tortillas according to package directions. Arrange 2 lettuce leaves on each tortilla. Spoon 2/3 cup steak mixture down center of each tortilla; roll up.