In a food processor or blender, combine the chickpeas, tahini, lemon juice, cumin, olive oil, salt & pepper. Drizzle water a tablespoon at a time to smooth out and reach the desired texture. (Hummus can be made a day in advance and stored in a sealed container in the refrigerator for up to 5 days.) Taste and adjust any of the ingredients as needed.
Place all the ingredients for the sauce in a blender or food processor and blend until smooth. Taste and season with salt and pepper, and adjust any ingredients as needed. Set aside.
Place the lettuce in the pita pocket, with turkey and hummus. Top with tomato and feta and drizzle the sauce. Serve with chips and pickle.