MIX oil, mustard, lemon zest, lemon juice, Worcestershire sauce, garlic, sugar and pepper in small bowl. Pour 1/4 cup of the mustard mixture over chicken in nonmetal bowl; toss to coat. Cover. Refrigerate at least 1 hour to marinate. Refrigerate remaining mustard mixture until ready to serve.
PREHEAT grill to medium-high heat. Drain chicken; discard marinade. Grill chicken 10 to 15 min. or until cooked through, turning once. Cut into thin strips.
TOSS chicken with lettuce, mushrooms, tomatoes and croutons in large bowl. Add reserved mustard mixture; mix lightly. Sprinkle with Parmesan cheese. Serve immediately.
