Leg of lamb is often eaten rare or medium-rare, but it can be cooked till well-done. For a bone-in leg of lamb, the cooking times and temperatures, after broiling, for a convection oven are: 1  Rare: internal temperature of 125 F, cook for roughly 11 to 12 minutes per pound.2  Medium-Rare: internal temperature of 130 to 135 F, cook for 15 minutes per pound.eg of lamb is often eaten rare or medium-rare, but it can be cooked till well-done. For a bone-in leg of lamb, the cooking times and temperatures, after broiling, for a convection oven are: 1  Rare: internal temperature of 125 F, cook for roughly 11 to 12 minutes per pound.