Have you tried the single ingredient foods like Natural Balance's Limited Ingredient Diet?
Dick Van Patten's Natural Balance® Allergy Formulas for Dogs
That may help if it is an allergy issue.
Still grain free.
I have noticed in posts some people here who like the Sweet Potato & Venison Formula and the Potato & Duck. Potato and Duck even has a Small Bites formula. If your dog likes lamb there is even Lamb & Brown rice.
Lower in protein too in case that is the issue with your fur baby.
I hope you can find out what the issue is