There have been several studies produced about the effects of lithium on humans, several are summarised in the Psychology Today's article Could You Have a Lithium Deficiency? (Deans, 2012). This article has links to several peer-reviewed surveys and articles that support the notion that trace amounts of lithium already present or added to drinking water can have beneficial neurological effects.
A couple of major examples are from studies performed in Japan and Texas.
A Japanese study Low-dose lithium uptake promotes longevity in humans and metazoans (Zarse et al. 2011), found that longevity is inferred by
Our findings indicate that low-dose Li+ exposure causes reduced mortality in C. elegans, and that these life span-extending capabilities of low-dose Li+ can be observationally translated into reduced overall mortality in humans that have been exposed to comparable amounts of Li+ in a similar long-term fashion.
Note: as the authors mention, directly testing the longevity on humans was impractical for their study, so they used a widely used analogue C. elegans.
In terms of decreasing the rates of suicide, a direct study was made for the article Lithium levels in drinking water and risk of suicide. (Ohgami et al. 2009), who, in their abstract stated that:
We found that lithium levels were significantly and negatively associated with SMR averages for 2002-2006. These findings suggest that even very low levels of lithium in drinking water may play a role in reducing suicide risk within the general population.
The SMR they refer to is the suicide standardised mortality rate.
An earlier wider study performed in Texas in the article Lithium in drinking water and the incidences of crimes, suicides, and arrests related to drug addictions. (Schrauzer and Stresther, 1990), found that there is a statistically significant case that:
Using data for 27 Texas counties from 1978-1987, it is shown that the incidence rates of suicide, homicide, and rape are significantly higher in counties whose drinking water supplies contain little or no lithium than in counties with water lithium levels ranging from 70-170 micrograms/L
A more recent article from a study performed in Greece, Lithium in the Public Water Supply and Suicide Mortality in Greece (Giotakis et al. 2013), concluded that
The results indicate that there is a tendency for lower suicide rates in the prefectures with high levels of lithium in drinking water