I read that lead poisoning does not correlate with murder rates in other countries so well.
The homicide rate is much lower in general in most other developed democratic nations, due to lack of guns.
Lead exposure could be a factors that emerges most in the context of guns that make killing so quick and easy and requiring only a half second of rage.
Guns make homicide many many times more likely because it makes killing many time easier and quicker than other methods. A half second of rage and lack of self-control and the guy across the room is dead. If lead poisoning leads to short-lived spikes in rage and negative spikes in self-control, then it would increase the odds that an available gun is used to commit a homicide. Also, if it just makes some people more generally violent, it will make them more homicidal but mostly if they have a gun since killing without one takes more skill, time, and/or planning. IOW, it is quite plausible that gun availability has both a general impact on massively increasing homicides, but also that it serves as an enabling condition that allows other factors to lead to homicide that otherwise would only lead to lesser aggression.
However, other nations do have other non-lethal crimes not impacted by gun availability. The OP research shows that in 9 countries, lead exposure over time predicts an 18 year lagged fluctuation in burglary and robbery (non-linear correlation coefficients in the .70-.90 range), and also assault in both the US and Britain.
Here is a link to an extensive paper with many analyses.
BTW, both race and SES independently relate to lead exposure, thus it probably can also account for some of the differences in violent crime related to those variables as well. A variable that can account for different group level comparisons, plus account for whole population fluctuation over time is compelling as a plausible causal factor, especially if it tracks the outcome variable in a complex non-linear pattern as shown in the OP.
Lead graph is bit weird, why does it have a dip between 1916 and 1956?
Prevalence of using lead paint peaked up until just after 1900 and then fell dramatically. However, from the 1950s to 1970s exposure to lead from gas fumes skyrocketed, especially in the denser cities. The author claims that the phase out of leaded gas in the 1980s is why the much higher murder rate in the biggest cities (over 1 million people) dropped down to similar levels of homicides as medium cities with 250K to 1 million. He also shows that independent of city size and lead gas exposure, differences in violence between cities of similar size can be partly explained by the differences in the lead paint exposure in sub-standard slum housing that was built around 1900 and not well maintained, removed, or at least painted over, so that by 1950s-1970s the paint was chipping and mixing with dust and being ingested by the kids.
