Combine all of the marinade ingredients (the anchovies, olive oil, garlic, lemon zest and thyme) in a pestle and mortar or a food processor. Blitz until you have a paste. Smother the lamb with this paste, and leave to marinate for at least an hour in the fridge.
For the green sauce, combine all of the ingredients and blitz in a food processor until well combined but not completely smooth. Set aside at room temperature until it's time to serve the dish.
After marinating, heat the remaining olive oil in a large frying pan on a medium heat. Add the lamb and cook, turning regularly, until cooked through. Serve with the green sauce.
