In a large mixing bowl, combine the shredded chicken, mayonnaise, Greek yogurt, Dijon mustard, and lemon juice. Mix until well combined.
Add the chopped celery, red onion, sweet pickle relish, garlic powder, salt, and pepper. Stir until all ingredients are evenly incorporated.
Taste and adjust seasoning if necessary, adding more salt, pepper, or lemon juice as desired.
Chill the chicken salad in the refrigerator for at least 30 minutes to allow the flavors to meld.
To assemble the sandwiches, place a generous scoop of the chicken salad on a slice of whole grain bread. Top with lettuce and tomato slices if desired, then cover with another slice of bread.
Cut the sandwich in half and serve immediately, or wrap it up for later.