I can only refer to my personal experience:
Hair test back in 2013 showed Iodine very high and Lithium very low.
How on earth would I have very high iodine levels? I don't live at the coast and don't consume seafood often. The salt is iodized, that's it. And I have Hashimoto's.
If I drink lithium-containing water I immediately feel hypo symptoms (I get cold hands and feet), so I have no intention of supplementing with Li.
My husband doesn't have thyroid problems or CFS but he started supplementing with iodine out of curiousiy and felt a boost of energy on it. We did his hair test and just got the results today: his iodine levels came back toxic through the roof (also for selenium which he taking along with iodine). So once again, I only see a direct link to excess intake and no evidence for inverse correlation.
One can get quite a bit of iodine from iodized salt. Also, iodine deficiency actually appears to be more prevalent in coastal areas, which was counter-intuitive to me but it has something to do with coastal soil depletion. Iodine also comes from bread and dairy. My guess is that in Hashimoto's it would also be released into blood from thyroglobulin destruction or from the deiodination of supplemental thyroid hormones.
There are some clearly documented problems with increased iodine intake.
1. In 1996 iodized salt was introduced in China, which resulted in increased iodine consumption. In a 1999 a study reported an increase in the incidence of autoimmune thyroiditis, overt hypothyroidism, and subclinical hypothyroidism in three regions of China. As their iodine intake increased, the incidence of thyroid conditions increased proportionately.
2. A more recent study which examined the Chinese population also showed that the incidence of subclinical thyroid disorder was higher in areas of the country(Rongxing and Chengshan) in which iodine consumption was higher. (3) In Ronxing area, higher iodine intake was attributed to higher iodine concentration in drinking water there. In addition to an increase in the incidence of hypothyroidism in this area, the incidence of autoimmune thyroiditis was also higher.
Mercola writes on his blog about a study that showed even 400 mcg of supplemental iodine per day can lead to subclinical hypothyroidism.
Clearly, iodine is one of the most controversial and debated topics in thyroid community. We each have choose for ourselves what side we want to bet on.