Place the drained canned tuna in a medium mixing bowl and use a fork to break it into small flakes.
Add the finely chopped celery, minced red onion, chopped dill pickle, and chopped fresh parsley to the bowl with the tuna and toss lightly to combine.
In a small bowl, whisk together the mayonnaise, Dijon mustard, and fresh lemon juice until smooth.
Pour the mayonnaise mixture over the tuna and vegetables, then sprinkle in the salt and freshly ground black pepper.
Stir gently until everything is evenly coated and the tuna salad is creamy but still holds its shape; taste and adjust seasoning with more salt, pepper, or lemon juice if needed.
Cover the bowl and chill the tuna salad in the refrigerator for at least 10 minutes to let the flavors meld.
When ready to serve, arrange the crackers in a single layer on a serving platter.
Spoon a heaping tablespoon of tuna salad onto each cracker, shaping it into a small mound so it sits securely.
Lightly sprinkle the tops with a pinch of paprika if using, and serve the tuna salad on crackers immediately before the crackers soften.