Trim fat from beef; slice into 1/4-inch strips. Set aside.
Combine the mustard, black pepper, garlic, and salt in a large bowl. Add beef, tossing to coat.
Place a large nonstick skillet coated with cooking spray over medium-high heat until hot. Add beef mixture; sauté 4 minutes or until done. Remove from pan; keep warm. Add mushrooms, onion, and bell pepper to pan; sauté 2 minutes. Add water; cover and cook 5 minutes, stirring occasionally. Stir in beef mixture and vinegar. Remove from heat; stir in cheese.
Warm tortillas according to package instructions. Spoon 1 cup mixture onto each tortilla; top each serving with 1/2 cup lettuce, and roll up.