Mix steak sauce, 2 Tbsp. lemon juice, oil and 1 tsp. garlic; pour 1/4 cup over steak in shallow dish. Turn steak to evenly coat both sides. Refrigerate 30 min. to marinate.
Heat grill to medium heat. Remove steak from marinade; discard marinade. Grill steak 10 to 12 min. or until medium doneness (160 degrees F), turning after 6 min. Meanwhile, mix remaining lemon juice, garlic, sour cream and dill in medium bowl. Cut cucumber slices in half. Add to sour cream mixture with onions and cheese; mix lightly.
Transfer steak to cutting board; let stand 5 min. Cut steak across the grain into thin slices; drizzle with remaining steak sauce mixture. Serve in pitas topped with cucumber salad.