I just looked in PubMed (a free database of medical articles), using the search strategy «dietary treatment Hashimoto's» and came up with some interesting articles, mainly about using selenium supplementation for
treatment of subclinical hypothyroidism in patients with Hashimoto's thyroiditis:
Treatment with zinc improved thyroid function and reduced the incidence
of subclinical hypothyroidism in patients with Down syndrome, who have an increased risk of hypothyroidism (6).
This study discovered administering T4 to patients with «high - normal» TSH (2 - 4 uIU / mL) lowered their cholesterol, supporting the existence
of a subclinical hypothyroidism with tangible harms, and numerous citing papers argue for a narrower reference range.
«Future studies should investigate whether screening for and treatment of subclinical hypothyroidism [mildly low thyroid function] is beneficial in subjects at risk of developing diabetes.»
Also, TSH ranges on conventional lab tests may fail to pick up some
cases of subclinical hypothyroidism or impending cases of autoimmune thyroid conditions, otherwise termed Hashimoto's Thyroiditis, which is the most common cause of hypothyroidism.