I trim "most of" the fat off... never ALL! I recommend (and use) a digital probe thermometer that I insert through the meaty part of the rack. When it registers 130 I pull the pan. The meat will continue to cook as it rests (while you make the sauce with the pan juices. You can leave the probe in and turned on to see how much more temp it absorbs.
We enjoy rack of lamb coated with a poultice of mustard and chopped fresh garlic and herbs. Add a little freshly ground pepper. No need for salt at all. The mustard takes care of it.