Preheat a charcoal grill. Lightly brush the onion pieces with olive oil and season with salt and pepper. Add the onion and lemon slices to the grill, placing the lemon slices around the perimeter so they don't scorch. Grill the lemon, turning, until lightly browned, about 1 minute. Grill the onion, turning, until browned, 6 to 8 minutes. Transfer to a plate to cool.
Chop the lemons and onions together until a coarse paste forms; transfer to a bowl. Mix in the olives, parsley, oregano, garlic and 6 tablespoons olive oil; season with pepper.
Rub the lamb chops lightly with olive oil and season generously with salt and pepper. Grill, turning once, for 5 minutes, then flip onto their edges (fatty and bone sides) and cook until browned, about 1 minute per side for medium-rare. Let rest for 2 minutes. Serve with lemon relish.