In a blender, combine the onion, garlic, parsley sprigs, lemon zest, lemon juice, allspice, salt and saffron and puree until smooth. Transfer the marinade to a resealable plastic bag, add the cubed lamb and turn to coat. Seal the bag, pressing out any air. Refrigerate the lamb for at least 6 hours or preferably overnight.
Light a grill or preheat a grill pan. Drain the lamb, shaking off the excess marinade. Thread the lamb onto 4 long skewers, leaving a bit of room between the cubes. Brush the lamb with the oil and grill over high heat, turning occasionally, until lightly charred, about 5 minutes for medium-rare meat. Serve the lamb skewers with warm pita and yogurt.