According to Serious Eats, it's fine to reheat sections of lamb using the same oven temperature in which the meat was cooked. A microwave on low is handy for heating up smaller individual slices of lamb. Leave the lamb in until its internal temperature indicates the desired level of doneness.
Medium-rare lamb should be reheated until its temperature is 130 degrees Fahrenheit. An appropriate temperature for medium lamb is 140 degrees. At higher internal temperatures, the meat dries out and becomes tough, chewy and flavorless.
For maximum flavor and moisture, Serious Eats recommends slow-cooking lamb at 200 degrees. When it's almost at the correct internal temperature, the oven should be turned up high for 15 minutes. This finishes cooking the lamb while crisping its external fat.
