Add the sugar and apple cider vinegar to a pan on low heat. Wait, without stirring, for the sugar to dissolve. At that point, the mixture will be bubbling. Allow it to bubble for 30 seconds, then remove from heat.

Pour the caramelized sugar, a ¼ cup of apple cider vinegar, lemon juice, grated apple, salt, pepper, apple juice and olive oil to a jar, cover, shake and pour over salad immediately before serving.