Mix dressing and steak sauce until blended; pour 1/2 cup dressing mixture over steak in shallow glass dish. Refrigerate 30 min. to marinate, turning after 15 min. Reserve remaining dressing mixture for later use.
Heat grill to medium-high heat.
Remove steak from marinade; discard marinade.
Grill steak 6 min. on each side or until medium doneness (160F). Meanwhile, heat reserved dressing mixture just until warmed. Cover large serving platter with lettuce; top with tomatoes and cucumbers.
Cut steak into thin slices; arrange over salad.
Drizzle with warm dressing mixture just before serving; sprinkle with cheese.