Combine oil, lemon juice, mustard, garlic, oregano and pepper in a plastic food-storage bag; Place lamb in bag, seal and refrigerate 6 to 24 hours.
Heat broiler. Drain lamb, reserving any marinade. Place lamb on a rack in a roasting pan.
Broil 6 inches from heat, 15 minutes on each side. Baste meat once or twice with reserved marinade. Tent foil over lamb and continue cooking 10 to 15 minutes more or until an instant-read thermometer registers an internal temperature of 145 degrees F. for medium-rare or 160 degrees F. for medium. Remove lamb; let stand, covered with foil, 10 minutes before slicing.
To Grill Lamb: Prepare a charcoal grill with hot coals, or heat a gas grill to high. Place lamb on grill rack and sear, turning once, until well browned on both sides, about 10 minutes total. Lower heat to medium or move lamb to cooler edge of grill; cook 15 to 20 minutes longer or to desired doneness. Baste meat once or twice with reserved marinade. Remove lamb; let stand, covered with foil, 10 minutes before slicing.