The length of time to cook a leg of lamb depends on whether you want them rare, medium or well-done.   For instance, you can cook a leg of lamb for 15 minutes per pound or until internal temperature registers 125 degrees F for rare. Cook it 20 minutes per pound or until internal temperature registers 130°F to 135°F for medium-rare. For medium, cook a leg of lamb for 25 minutes per pound or until internal temperature registers 135°F to 140°F. Finally, cook 30 minutes per pound or until internal temperature registers 155°F to 165°F to make it well – done.