Boil diced potatoes in salted water until fork-tender, about 10–12 minutes. Drain and let cool slightly.
While potatoes cook, boil the eggs until hard-boiled, about 10 minutes. Cool, peel, and slice them.
In a small bowl, whisk together mayonnaise, lemon juice, Dijon mustard, salt, and pepper to make the dressing.
In a large mixing bowl, combine cooled potatoes, drained tuna, chopped celery, red onion, and parsley.
Pour the dressing over the salad and gently toss to coat. Fold in sliced eggs carefully.
Serve immediately or chill for a few hours to allow the flavors to blend.