Place lamb on a greased foil-lined baking sheet. Drape a piece of heavy-duty foil over bones to prevent overbrowning. In a small bowl, combine the honey, preserves, oil and lime juice. Set aside 1/2 cup. Spoon half of the remaining glaze over lamb.
Broil 4-6 in. from the heat for 10-12 minutes or until meat reaches desired doneness (for medium-rare, a thermometer should read 135°; medium, 140°; medium-well, 145°), basting once with remaining glaze.
Remove lamb from the oven and loosely cover with foil. Let stand for 5 minutes before cutting. Brush with reserved glaze.