Combine all marinate ingredients (except rosemary and only using half of divided salt) and whisk together.
Place lamb in sealable plastic bag and pour marinade over lamb, reserving ¼ cup. Seal bag and massage to ensure lamb is completely coated. Place sealed bag and reserved marinade in refrigerator for at least four hours, turning occasionally.
Remove lamb from refrigerator and place on countertop to allow meat to slightly come up to room temperature. Light grill and set for two-zone heating. Close lid on grill and establish temperature at 350°F.
Remove lamb from bag, and sprinkle with roughly chopped rosemary. Insert reliable leave in thermometer probe and place lamb on grill over indirect heat. Close lid and cook using indirect heat until internal temperature reaches 90°F. Using a basting brush, coat the lamb with reserved marinade. Close lid and continue to cook over indirect heat until meat reaches 120°F.
Once meat reaches 120°F, move the rack of lamb from indirect heat to directly over the coals in order to achieve a nice sear on both sides.
Remove lamb from grill, tent with aluminum foil and allow to rest five minutes before slicing.
Slice lamb into individual chops and sprinkle with remaining sea salt (or more to taste) and serve.