Open both tuna cans and press the lid firmly against the fish over the sink for 30 seconds. Drain through a fine-mesh sieve and press again until the tuna feels dry.
In a medium mixing bowl, whisk together the mayonnaise, Dijon mustard, lemon juice, salt, and pepper until smooth. Taste and adjust before adding anything else.
Add the drained tuna. Use a fork to flake it into the dressing while folding — not stirring.
Add the celery, red onion, relish, and dill. Fold until evenly combined.
Taste and adjust lemon juice or salt as needed. Refrigerate for 20 minutes before serving if time allows.