Rare lamb is actually the Chefs preferred way to serve lamb, not everyone likes rare, 125⁰F, but most people will eat a medium rare lamb chop. Two things about cooking lamb rare which are important when deciding what temperature range to cook the lamb to. First is lamb cooked rare has a milder flavor because the fat in the chops hasn’t melted and incorporated into the meat, second is the meat hasn’t cooked long enough for the protein strands to shrink and solidify, making a more tender chop. If you can eat it rare, I recommend you do so, if you can’t, then don’t cook it past medium rare, and pull it as soon as it gets to temperature.