Cook the Eggs: Put the eggs in a large saucepan and cover with cold water. Bring to a boil over high heat, then cover with a lid and remove from the heat. Let stand for 12 minutes, then place in ice water and let them cool for 5 minutes.
Prepare the Eggs: Peel the eggs and transfer them to a bowl. Chop or mash as desired.
Finish the Dish: Add the celery, onion, mayonnaise, lemon juice, mustard, salt, and pepper; mix thoroughly until well blended. Taste and adjust seasonings with more salt if needed, or add more mayonnaise for a creamier texture.
Serve: Serve the egg salad in sandwiches or mound it on lettuce leaves for a lighter luncheon salad.