COMBINE pesto and vinegar in medium bowl; reserve 1/2 cup mixture for dressing.
PLACE lamb in large, glass baking dish. With tip of sharp small knife held at 45-degree angle, cut 1/2-inch slits all over lamb. Pour 1/2 cup pesto mixture over lamb, rubbing marinade into slits. Marinate at room temperature for 1 hour.
PREHEAT grill to medium.
GRILL lamb for 20 to 30 minutes, turning every 5 minutes and basting with 1/2 cup pesto mixture or until instant-read thermometer inserted into thickest part of lamb reads 125° F (medium-rare.) Remove from grill; let stand for 10 minutes. Cut lamb into 1/2-inch-thick slices.
PLACE salad greens on large serving platter. Top with lamb slices; and drizzle with reserved 1/2 cup pesto mixture. Sprinkle with cheese.