Place the mushrooms in a ceramic dish. Cut the lamb into long thin strips or cubes and thread onto skewers. Combine lemon juice, oregano, garlic, onion, paprika, olive oil and salt and pepper in a jug, whisk well to combine. Pour half over the mushrooms and half over the lamb. Turn to coat. Cover. Refrigerate for 30 minutes if time permits.
Preheat barbecue plate and grill on medium-high. Barbecue the lamb on the grill for 4-5 minutes turning often for medium or until cooked to your liking. Barbecue the mushrooms on the plate for 3-4 minutes, turning until light golden and tender.
Place skewers onto plates, spoon over the mushrooms and serve with pita bread, tzatziki and lemon wedges.