Season the lamb chops well with salt and pepper. In a 10-inch skillet, heat butter and olive oil over medium-high heat. When the butter has melted, add the chops and sear (without moving) until well browned on one side, about 3 minutes. Flip the chops and sear the second side for about 3 minutes. They should have a deep-brown crust but will be pink (medium-rare) in the middle. Remove to a plate and cover loosely with foil. Let rest a few minutes before serving warm.