Combine tuna and diced celery in a bowl, and toss gently. Combine salad dressing, lemon juice, and dill, stirring well. Add to tuna mixture, tossing gently.
Trim crusts from bread; flatten each slice of bread to 1/8-inch thickness using a rolling pin. Spread 2 tablespoons tuna mixture evenly over each slice. Roll up; wrap in plastic wrap. Chill.