I am not really suggesting any particular cause of poverty, but lead-soil levels seem to have some negative effect. The more important suggestion is that its not just income disparity, anonymity and juxtaposition of poverty and wealth, if at all, that leads to higher crime rates in cities.
In fact, mixed-income neighborhoods have been linked to better social mobility, but that is getting off-topic.
I think your conclusion, from correlation between lead concentration in soils to conclusiong "lead-soil levels seem to have some negative effect" -- is entirely unjustified.
The alternate hypothesis I mentioned seems as, or more, plasuble. That it's not lead-soil levels that are having any effect at all, but rather that lead-producing activities are socially undesirable, and end up in poor neighborhoods because poor people lack political power.
I suppose the scientific method would be to devise an experiment or investigation that would attempt to distinguish between these two hypothesis. Possibly people already have, and arguing about it in the academic literature now.
One danger of concluding causation from correlation in the 'big data' era is how easy it is to go hunting for correlations. If I test ketchup consumption against 1000 other variables, it may be fairly likely that I'll find a correlation against at least one of them. (If I flip a coin 10 times; and then do this experiment 1000 times, it's not unlikely that at least one of those 10-times iterations I'll get 10 ten heads). So maybe I find that ketchup consumption is very closely correlated with public transit availability, across cultures and times and governments. That doesn't really mean that ketchup causes public transit or vice versa, it just means that if you have enough data, you're going to find happenstance correlations.
Most of my previous comments were quite non-committal. For instance, the phrase "lead-soil levels seem to have some negative effect" was cherry-picked for your analysis, and given much stronger meaning than intended. First, let's examine the word choice of "seem". It means "give the impression or sensation of being something or having a particular quality." This modifies the statement, to imply that the data "gives the impression" that there is "some negative effect". This is a much weaker statement than a hypothesis on the effect of lead-soil levels on poverty-stricken neighborhood. Perhaps, that statement would have been more clear if written as, "lead-soil levels seem to have an effect on crime". The implication from the sentence that follows is that the value of "some" is "crime".
It very well could be that lack of political power caused lead-producing activities to be concentrated in low-income neighborhoods. However, the issue at hand is not that lead-soil levels cause poverty; it's that lead-soil levels increase the incidence of crime. This point may not have been clear, as conceded above.
Indeed, correlation does not imply causation, but we know much about the health effects of lead [1] and its impact on decision making. We know that the correlation of crime rates with increasing and decreasing lead-levels, in a variety of situations, throughout many policies and governments, holds. We know both a pathway and have a strong correlation. Dismissing this as happenstance is unwise.