Preheat oven to 400 degrees F.
Combine lemon zest, oregano, 3/4 teaspoon salt and pepper in a small bowl. Rub the mixture onto both sides of lamb chops and set aside for at least 10 minutes or refrigerate for up to 1 hour.
Meanwhile, combine tahini, yogurt, cucumber, lemon juice, garlic, parsley and the remaining 1/2 teaspoon salt in a small bowl. Whisk in enough water to thin the sauce to desired consistency.
Heat oil in a large ovenproof nonstick skillet over medium-high heat. Add the lamb chops and cook until browned on one side, about 2 minutes. Turn them over and transfer the pan to the oven. Roast until an instant-read thermometer inserted horizontally into a chop registers 135 degrees F for medium-rare, 8 to 14 minutes, depending on thickness. Serve the chops with the tahini sauce.
Make Ahead Tip: Prepare sauce (Step 3), cover and refrigerate for up to 3 days. Prepare rub and rub onto lamb chops (Step 2) and refrigerate for up to 1 hour.
Tip: Tahini is a thick paste of ground sesame seeds. Look for it in large supermarkets in the Middle Eastern section or near other nut butters.
1/2 other carbohydrate, 3 lean meat, 2 fat