Strain the broth into a large saucepan and skim off the fat. Bring the broth to a boil. Add the diced celery and cook for 3 minutes. Add the diced carrots and cook for 5 minutes. Add the potatoes and cook for 5 minutes. Season the reserved breast meat with salt and pepper, add it to the soup and simmer until it is cooked through and the vegetables are tender, about 5 minutes. Season the soup with salt and pepper, sprinkle with parsley and serve in bowls. Pass the lemon wedges at the table.