I won't discount that therapeutic doses may have such side-effects, but the question is whether that is relevant to the present discussion. I claim that the side effect of being docile would not occur at a dosage of 100 times smaller than therapeutic doses. Maybe there is such a thing as a "1/100th as docile" effect, but it doesn't always make sense to extrapolate effects linearly; it can also be that the effect just isn't there. The way I arrive at that intuition is by making an analogy with water: you can drown in a bathtub of water, but no person can drown in a droplet of water.

You call it "simple reasoning" to make your inference about microdosing, but actually we have no idea how lithium even affects the brain / mind, so it's not possible to arrive at the conclusion by reason. It would have to come from evidence from controlled studies, and I believe these indicate that side-effects are restricted to high doses.

Also, "practically no chance of suicide" -- you can't be serious about that; no drug can guarantee or even come close to that.

You already have salt with and without iodine, so no, wouldn't be difficult to avoid. Whether you should call it "medication" is debatable; giving someone vitamin C is not necessarily medication, it can be a food supplement. The same could be argued for lithium which occurs naturally in certain water springs.