Not all lamb is created equal. A rack of lamb or a leg of lamb is best at medium-rare. But ground lamb for burgers or meatballs? Cook that to 160°F. Safety first, because grinding introduces more surface bacteria.
Lamb chops? Rare or medium-rare, no contest. Shoulder? Low and slow, baby. Braise that thing until it falls apart. Different cuts, different rules.
Don’t overthink it. Just match the temp to the cut and your taste. Easy peasy.