1) In a dish large enough to hold the lamb chops in a single layer, combine half of the lemon juice, the olive oil, rosemary, garlic, one teaspoon of salt and pepper. Add the lamb, turn to coat with the marinade and set aside for about 15 minutes at room temperature or up to two hours in the refrigerator.
2) Preheat a large frying-pan over medium-high heat for about one minute. Pat the chops dry and season on one side with salt and pepper. Add enough oil to lightly coat the surface of the pan. Working in batches if needed, add the chops to the pan, seasoned side down. Cook until crisp and brown, about two to three minutes. Season the top side with salt and pepper, turn, and continue cooking until just firm and an instant-read thermometer registers 58°C, about one to two minutes. Transfer to a platter and tent with foil to keep warm. Allow the chops to rest for 5 to 10 minutes.
3) Pour off any fat left in the pan. Return the frying-pan to medium heat. Add the chicken stock and scrape up the brown bits on the bottom of the pan with a wooden spoon. Add the remaining lemon juice and simmer until the mixture is reduced to a glaze, about four minutes. Swirl in 30g of the butter. Add the basil and olives and season. Return the lamb chops to the pan and toss to coat thoroughly with the sauce.
Arrange the chops on a platter, pour over the sauce and garnish with basil leaves.