In a small skillet heat 1 tablespoon of the oil. Add the celery, garlic, onion and cook until tender, about 5 minutes. Transfer to a bowl and let cool.
Mix the chicken, dill, poultry seasoning into the vegetable mixture, season to taste with salt and pepper. Form into 6 patties.
In the same skillet, heat the remaining 1 tablespoon of oil over medium heat. Add the patties and cook, only turning once until firm, about 15 minutes. Remove to a plate.
Add the butter to the skillet to melt and mix in wing sauce. Add the patties back into the skillet and turn to coat, spoon sauce onto top of patty then top with blue cheese then cheddar slice. Cover skillet, turn heat off and let stand until cheese is melted.
Toast sandwhich thins, top each patty with lettuce and enjoy!