In a medium bowl, combine the lamb, one-third of the onion, 1 tsp. each paprika and salt and 1/2 tsp. pepper. Form the mixture into a patty.
Preheat a grill to medium. In a small bowl, combine the EVOO, lemon zest and the remaining 1 tsp. paprika. Drizzle the seasoned oil on a baking sheet; turn the dough disks in the oil. Press each disk into a 6-inch round.
Place the lamb patty on the grill and cook, turning once, for 5 minutes. Meanwhile, place the dough on the grill, cover and cook until it bubbles on top and grill marks appear underneath, about 3 minutes. Flip the crusts and, working quickly, top with the tomato slices and remaining onion. Cover and cook until baked through, about 3 minutes.
Finely chop the grilled lamb and sprinkle on the pizzas; top with the parsley. Serve with the lemon wedges.