Drain the tuna and mix with the butter. Season with salt, pepper and lemon juice. Drain capers, rinse the parsley, pat dry and chop both. Stir parsley and capers into the tuna.
Rinse, trim and slice the tomatoes. Rinse celery, trim, reserve the leaves and finely chop the stalks. Toast the tramezzini bread and cover with the tomato slices. Spread with tuna. Distribute celery over the top and garnish with celery leaves. Serve immediately.