Mix olive oil, mustard, lemon juice, oregano, garlic, salt, and pepper together in a small bowl.
Place the whole rack of lamb into a large zip-top bag and pour mustard mixture all over it. Massage the sauce into the meat until fully coated. Place in the refrigerator for at least 3 hours, or up to 6 hours.
Clean an outdoor grill and preheat for high heat. Lightly oil the grate.
Remove lamb from the refrigerator and discard marinade. Wrap exposed bones in a layer of aluminum foil to prevent them from burning and flaking.
Place lamb on the preheated grill over direct heat. Sear the surface briefly, just until a dark brown crust starts to form, about 3 minutes; be careful it doesn't burn. Flip and sear the other side.
Move onto indirect heat and close the grill. Cook until an instant-read thermometer inserted into the center reads at least 120 degrees F (58 degrees C) for medium rare, 15 to 20 minutes.
Transfer lamb to a serving dish and cover with foil for 5 minutes. Remove all foil and cut into chops to serve.