Fill a large pot with water; add the onion and celery. Bring to a boil. After water is boiling, add the thawed wings and boil for 10 minutes.
While wings are boiling, combine brown sugar, soy sauce, lemon juice, garlic and ketchup in a bowl. Set aside.
Take the wings out of the water and place them in a large pan or plastic container. To use a large, resealable plastic bag, let wings cool slightly first. Pour sauce over the wings. Place them in the fridge for a minimum of 3 hours, stirring occasionally. (It is recommend refrigerating the wings overnight.)
Once wings have marinated, coat a cookie sheet that has a lip on it with nonstick spray. (For easier cleanup, cover the pan with aluminum foil.) Add wings; bake at 325°F for 1 hour.