A city with no-to-little elemental lithium would need to add 70 micrograms/L of elemental lithium to the water supply. Since we're adding lithium carbonate (not pure lithium), we would need roughly 200 micrograms/L. (For reference, there are a million micrograms in a gram).
The average Canadian domestic user uses just over 100,000 L of water a year (Source). At 200 micrograms/L, we would need to add roughly 20 grams per person of lithium carbonate for a total cost of $1.53 per person, or $153,000 per 100,000 people.
The city of Toronto has 3.3 murders/100,000 people (Source). A 30% reduction in this rate would lower it by 1 murder per year per 100,000 people. If our rough back-of-the-envelope calculations are correct and the lithium carbonate method works like the Texas study suggests, $153,000 buys us one less murder. That does not take into account the reductions in rapes, suicides, drug use or thefts.
Will it work? I don't know. It seems like it would be worthy a pilot study or two. Although those levels of elemental lithium are believed to be safe, there may be side-effects we are not considering. There are ethical considerations as well, but it is hard to make a case that adding fluoride to the water supply is ethical but lithium is not - and we've been adding fluoride to drinking water for over half a century.
My first reaction is to note that Lithium is clearly a mind-altering drug and there does seem to be a basic principle that adding mind altering drugs to the water supply is a generally bad idea. Heck, the theme of the Firefly movies (Serenity) was all about a plan like this going very, very wrong. Or, more realistically, one could easily imagine the addition of sedatives to the water as being a response to political unrest (and this would also reduce the murder rate).
Furthermore, the original (ecological) study in Texas was based on naturally occurring Lithium in the water. This brings up two questions to me:
1) Is the distribution of Lithium independent of the characteristics of the inhabitants? This is necessary to make sure that this is not a confounding effect, of some kind (another way to say the same thing is whether water supply is a valid instrument for an instrumental variables analysis).
2) Is the causal agent lithium, or is it another substance that is associated with Lithium?
It is a complex question but it is very effective at making us evaluate our intuitions on public health intervention. Go read . . .