If that correlation did indicate a causal relationship, it would imply that there is a large range of individual 'thresholds' for the the environmental lead level to trigger violent criminal activity two or three decades later. Although not impossible, that would perhaps be a little surprising - one might expect that it would be more likely that the ('quantitative') 'severity' of violent criminal behaviour, rather than the number of individuals committing violent crimes, would correlate with (quantitative) levels of lead in the environment (hence body).
Let's take it in pieces.
Is it believable that lead damages the brains of children and babies?
Is it believable that damage, affecting children's developing brains was highest where lead contamination was highest?
Is it believable that lead contamination was highest in city centres and districts with a lot of road traffic?
Is it believable that brain damage can lead to behavioural disorders and violence?
Is it believable that violent crime and murder rates were higher in city centres and districts with lots of road traffic?
Is it believable that violent crime rose when the brain-damaged babies and children grew to adulthood? And dropped when the supply of brain-damaged babies and children dropped?
Is it believable that this would happen, with the same time lag, in different US states and in different countries of the world, as different dates according to the date when leaded petrol was removed from sale?
Is it believable that alternative causes for the correlation have been investigated and disproved?
Is it believable that when you study the research, you will find that the above eight possibilities have already been researched and proven?
If so, we have not so much to contend over.
When a change in behaviour (e.g. criminality) occurs, it can be due to various things. The pattern and speed that it occurs gives strong clues as to the cause.
I'm thinking of the possibility that smoking cigarettes causes lung cancer. IIRC, the original study published in the Lancet some 60 years ago was based on two things: A survey of GPs to see which of them smoked; and subsequent research to see which of them had died of lung cancer. The correlation was convincing enough that most smoking GPs stopped. The tobacco and advertising trades both spent many years, and billions of dollars, trying to fight the truth. Last I heard, they were still winning in China and some other countries where the government has priorities other than the lives and health of its citizens. In the same way, there are still countries that permit leaded petrol (the Tetraethyl lead is profitably produced and exported from the UK by an American-owned company, which is another scandal. The company has previously been convicted of bribing foreign officials in impoverished nations).