Place the chicken along with the salt, pepper, onion, and celery stalks in a large stock pot. Cover with water and bring to a boil. Lower the heat and simmer until the chicken is cooked through. Remove chicken from pot, cool, and remove skin and bones. Reserve the liquid. Dice the chicken and place in a large bowl. Add the chopped celery, eggs, seasoning salt, mayonnaise, lemon-pepper, pepper, and some reserved stock and mix well.