In a mixing bowl, combine the cooked chicken, mayonnaise, celery, red onion, dill, lemon juice, salt, and pepper. Mix well until all ingredients are evenly coated.

Lay out 4 slices of bread on a clean surface. Spoon the chicken salad mixture evenly onto each slice.

Top each sandwich with a lettuce leaf and a slice of tomato if desired. Place the remaining slices of bread on top to close the sandwiches.

Cut the sandwiches in half and serve immediately, or wrap and refrigerate for later.