I prefer cooking lamb racks until the inside reaches 160 degrees F to get the medium-well in the center. To determine the internal temperature of the meat, it’s best to use a meat thermometer.  - If you’d like the lamb racks to be more on the rare side in that case the internal temperature should be at around 125 up to 135 degrees F.  - If you’d like to get it to medium-rare, the meat should be cooked to around 140-150 degrees F.  Always keep in mind that after you take the lamb out of the oven, it will continue cooking for a couple more minutes, so taking it out before it reaches the desired tempereature is always a good idea.