Earlier quoted context omitted.
People use it in much smaller dosages then it's usually prescribed to apparently beneficial effect. I believe its also in the water supply in certain places, so if it works for dementia there are natural experiments already running on this. https://www.psychiatrictimes.com/view/low-dose-lithium-a-new...
Yes, it's already thought that there's an association between naturally occurring lithium in drinking water and decreased suicide rates: https://www.cambridge.org/core/journals/the-british-journal-... I would think naturally occurring lithium in some people's water would give pretty good control conditions to do a wide study of this effect on Alzheimers as well?
These things are simple enough to advise the populace to use on their own. The government should never play nanny, ever.