Open both cans of tuna and drain in a fine-mesh strainer, pressing gently with a fork to remove as much liquid as possible. Let drain for 2-3 minutes.
Transfer the well-drained tuna to a medium mixing bowl and use a fork to gently flake it into small, even pieces.
Rinse the celery and pat completely dry. Dice into very small pieces (about 1/4 inch). Peel and finely mince the red onion. If using fresh parsley, wash, dry, and chop it finely.
Add the mayonnaise, fresh lemon juice, sweet pickle relish, Dijon mustard (if using), salt, and black pepper to the bowl with the tuna.
Gently fold everything together with a rubber spatula or large spoon until the tuna is evenly coated with the creamy dressing.
Add the finely diced celery, minced red onion, and fresh parsley (if using) to the tuna mixture. Fold gently to combine until all ingredients are evenly distributed.
Taste the tuna salad and adjust seasonings as needed, adding more salt, lemon juice, or mayonnaise to achieve the perfect balance.
Cover the bowl with plastic wrap or transfer to an airtight container. Refrigerate for at least 30 minutes before serving to allow flavors to meld.