In a medium bowl, combine shredded chicken breast, mayonnaise, Dijon mustard, lemon juice, chopped celery, chopped red onion, salt, and black pepper. Mix well until all ingredients are evenly incorporated to make the chicken salad.
Preheat a skillet or griddle over medium heat.
Butter one side of each slice of bread evenly with the softened butter.
Place two slices of bread, buttered side down, on the skillet. Toast until golden brown, about 3-4 minutes. Flip and toast the other side for 2-3 minutes. Remove and set aside.
Repeat the toasting process with the remaining two slices of bread.
To assemble the first layer of the sandwich, place one toasted bread slice on a clean surface, buttered side down. Spread half of the chicken salad evenly over the bread.
Top the chicken salad with two slices of cooked turkey breast and two leaves of romaine lettuce.
Place a second toasted bread slice on top, buttered side down. Spread the remaining chicken salad evenly over this slice.
Add two slices of tomato, two slices of cooked turkey bacon, and two leaves of romaine lettuce on top of the chicken salad.
Finish the sandwich by placing the last toasted bread slice on top, buttered side down.
Using a sharp knife, carefully cut the sandwich diagonally into quarters. Secure each quarter with a toothpick if desired.
Serve immediately and enjoy your Club Sandwich Ensalada de Pollo.