Whisk together the oil, garlic, cumin and oregano in a large bowl. Add the lamb, peppers and onions, and toss to combine. Cover and chill in the fridge for 2 hours, or overnight if possible.
Remove the lamb from the fridge 10 minutes before cooking and season. Preheat a griddle pan or barbecue to a high heat, then thread the marinated lamb onto the prepared skewers, alternating with pieces of pepper and onion.
Cook the kebabs for 7-10 minutes, turning regularly, until just cooked. Warm the pittas. Serve the kebabs with spoonfuls of tzatziki and slices of warm pitta bread – plus a little Greek salad if you wish.
