In a small bowl, soak the onions in cold water, for 15 minutes. Drain.
Meanwhile, in a large saucepan, with a tight-fitting lid, place the eggs and cover with cold water by 1 inch. Bring to a boil and cook for 1 minute. Cover the eggs, remove from the heat, and set aside for 8 minutes. Drain the water from the pan and cool the eggs in the pan under cold running water. Peel the eggs and cut into sixths.
In a large bowl, mix together the onion, celery, mayonnaise, dill, mustard, lemon juice, and salt.
Add the eggs to the mayonnaise mixture and gently mix them together. Season with pepper to taste. Use in sandwiches, with lettuce and tomatoes, or in a salad.