In a large bowl mix the ground lamb with the onion, garlic, allspice, coriander, cumin, salt and pepper.
Mix the ingredients using your hands until combined.
Divide the mixture into 8 pieces and shape each piece into a burger. Make an indentation in the middle of each burger using your finger.
Preheat the grill to medium high heat and brush the grates with vegetable oil. Place the burgers on the grates and grill for 5 minutes on each side, flipping once.
Make the yogurt sauce by mixing the yogurt, sumac, salt, pepper, lemon zest, vinegar and parsley in a bowl.
Assemble the burgers with buns, tomatoes, cucumbers, sumac onions and yogurt sauce.