For the chicken wings and brine: Combine the salt, sugar, vinegar and 5 cups water in a nonreactive container and stir until the salt and sugar are dissolved. Put the chicken wings in the brine and marinate, refrigerated, at least 12 hours.
For the pickled celery: Put the vinegar, sugar and pickling spice in a saucepot. Add the celery and bring to a boil over medium heat. Remove from the heat and let the celery cool in the pickling liquid. (You can also store the celery in the pickling liquid.)
For the wing glaze: Combine the honey, vinegar, soy sauce and lemon juice in a large bowl and mix thoroughly.
Preheat the oven to 375 degrees F.
Remove the wings from the brine and discard the brine. Put the wings in a roasting pan and bake until a meat thermometer inserted in the wings registers 165 degrees F, about 25 minutes. Toss the hot wings in the wing glaze to coat.
Serve with the pickled celery and your favorite dipping sauces.