Set grill for two-zone grilling targeting between 450 and 500 degrees Fahrenheit (F) over the direct heat.
Remove the sliver skin and excess cartilage from the lamb using a good boning knife. Coat with olive oil and dry rub.
Place the rack of lamb, meat side down over direct heat. Grill with lid closed for 5 - 6 minutes or until you see a nice sear. Flip and continue grilling the bone side of the lamb for 5 - 6 minutes until you see a nice sear. Finally stand the lamb up with the bones straight up to sear the third side for 3 - 4 minutes.
Move the lamb to indirect heat and finish grilling until the internal temperature of the lamb reaches 135 degrees F for medium rare using a good instant read thermometer.
Let rest for 10 minutes and then slice and serve with the jalapeño chimichurri sauce.