Place the cubed potatoes in a medium saucepan and cover with cold, salted water. Bring to a boil and cook for 15-20 minutes, or until fork-tender. Drain well and allow to cool slightly.

While the potatoes cool, prepare the dressing by whisking together the mayonnaise, Dijon mustard, lemon juice, dried dill, salt, and pepper in a medium bowl.

In a large mixing bowl, gently flake the drained tuna. Add the chopped celery and minced red onion to the bowl.

Add the slightly warm or room-temperature cooked potatoes to the tuna mixture. Folding gently is crucial here to prevent the potatoes from breaking down too much.

Pour the prepared dressing over the tuna and potato mixture. Fold everything together carefully until just combined. Taste and adjust seasoning (salt, pepper, or a squeeze of lemon) as needed.

For the best flavor, cover the salad and refrigerate for at least 30 minutes before serving. Serve chilled on lettuce leaves, in sandwiches, or as a side.