Brush the lamb all over with the curry paste. Cover and marinate at room temperature 20 minutes.
Meanwhile, combine the yoghurt, lime juice, mint and salt in a bowl; cover and store in the fridge until the lamb is ready.
BBQ the lamb, lightly oiling the cooking grate first if prone to sticking, 3-4 minutes per side, or until the desired doneness is achieved. Serve the lamb with the yoghurt alongside for dipping.