Here's Natural Balance LID page:
LID Limited Ingredient Diets Dry Dog Formulas - Natural Balance Pet Foods
NB is a potato or sweet potato heavy food...lots of potato can be a problem for yeasty dogs bc sugary foods are fuel for the yeast. So it would be a good idea to rule out yeast by doing a skin scraping. It's a very simple test, they take a skin sample & look under the microscope. An experienced Vet will be able to see right away if it's bacterial or yeast or both & treat it accordingly.
BTW, Nature's Variety is a very busy food, lots of different ingredients, def not a limited ingredient food.