In a small bowl, combine onion and vinegar. Let sit, uncovered, until onion turns a brighter pink, at least 15 minutes and up to 45 minutes. Drain well, reserving vinegar for another use, if desired.
In a medium bowl, whisk together labneh, mustard, lemon juice, za'atar, garlic powder, and salt. Fold in chicken, celery, and reserved onion and mix well to combine. Cover and refrigerate to let flavors meld for at least 30 minutes, up to 4 days.
To Assemble Sandwiches (optional): Spoon chicken salad onto bread slices, top with lettuce, then close with remaining slices.
