Peel and quarter potatoes. In a large pot, combine with salted water (2 quarts water to 2 tbsp salt). Bring to boil and simmer 10-12 minutes for fork-tender doneness.
Separate eggs for boiling. Place in saucepan, cover with water at room temperature. Bring to gentle boil, remove from heat, and let sit 9-11 minutes. Immediately transfer to ice bath for 5-minute shock cooling.
In chilled stainless steel bowl, whisk mayonnaise and Dijon mustard. Squeeze in juice from 1/2 lemon (about 1 tbsp) to brighten the dressing. Adjust seasoning in stages as you blend.
Finely dice chilled pickles and fold into dressing with chopped hard-boiled eggs. Toss with drained potatoes.
Add sliced celery and chopped red onion to the mixture. Fold gently to avoid crushing ingredients.
Chill for at least 30 minutes before serving to let flavors meld and achieve ideal texture.