Rub lamb with garlic, ½ cup lemon juice, half the oil and half the oregano. Place lamb in a large shallow dish, then cover and marinate in the fridge for 3 hours, preferably overnight.
When ready to cook, preheat oven to 140℃/284℉. Transfer lamb to a large baking dish and roast, uncovered, for 4 hours.
Meanwhile, place potatoes, lemon zest, fresh thyme, remaining lemon juice and remaining oil in a large mixing bowl, tossing gently to combine. Transfer potatoes to another baking tray, arrange in a single layer, then roast for last 40 minutes of lamb cooking time.
Remove lamb from oven and cover with foil to keep warm. Increase oven temperature to 200℃/390℉ and continue roasting potatoes for a further 20 minutes or until tender and cooked.
Meanwhile, place mixed salad leaves, tomato, cucumber, onion balsamic and remaining oregano in a salad bowl. Serve lamb with lemon potatoes, garden salad and yoghurt on the side.