Preheat oven to 400°F and line a rimmed sheet pan with parchment paper.
Grate the onion into a towel, squeeze out excess liquid, and combine with chicken, herbs, lemon zest, and spices.
Spread mixture evenly on the pan into a ½-inch thick rectangle. Slice into strips and separate slightly. Drizzle with olive oil.
Bake 15–20 minutes, until cooked through, then broil 1–2 minutes to brown on top.
Toss cucumber salad ingredients together and season with salt and pepper.
Spread hummus on lavash bread, add kefta strips, cucumber salad, and pickled onions. Wrap tightly and sear in a skillet for 1–2 minutes per side.
