Holistic does not necessarily mean hypoallergenic, and I have had plenty of dogs allergic to both lamb and rice. Unfortunately, there is no accurate skin
or blood test for food allergy in dogs
, the test and treatment is the hypoallergenic diet for 6-8 weeks with no other treats, table scraps, rawhides, milkbones, chewable supplements, etc.
The dermatitis, hairloss and odor that you are describing is likely a bacterial skin infection, secondary to allergies.