Place steak in a large shallow dish. Pour vinaigrette over it, turning to coat both sides. Cover and refrigerate several hours or overnight, turning once or twice. Lift steak from marinade, allowing excess to drain off. Sprinkle both sides of steak with black pepper.
For the Salsa-Sour Cream Sauce, stir together sour cream, salsa, and lime juice. Top with a chili pepper, if desired. Cover and chill until serving time. For the Honey Mustard-Yogurt Sauce, in a small bowl stir together honey mustard, yogurt, and dill weed. Cover and chill until serving. For the Horseradish-Mayo Sauce, in a small bowl stir together mayonnaise, horseradish, and chives. Top with additional pieces of chives. Cover and chill until serving time.
Grill steak over medium heat, turning once, until desired doneness, 12 to 15 minutes for medium. Let steak rest for 5 minutes, then slice across the grain into thin strips, about 1/4 inch thick. Loosely thread 2 or 3 strips onto 10- or 12-inch wooden skewers; add a grape or cherry tomato at the tip.
To assemble, open the two bunches of lettuce, keeping them intact. Place prepared lettuce on serving platter. Arrange the assembled skewers on top of the lettuce leaves. Place the cilantro sprigs and/or basil leaves in a small bowl. Place the dipping sauces in additional small bowls.
To serve, have guests tear off a lettuce leaf and top with an herb sprig. Then, top with a skewer of meat. Fold lettuce leaf around skewered meat and gently pull to remove skewer, holding lettuce roll securely. Serve with dipping sauce. Makes 6 main-dish servings.