Lott has also said "[A] nation's wealth [is maximized] if a crime is not deterred when the benefit to the criminal of a particular crime is greater than the total social cost of that crime." - a very Chicago School view of the world.
Therefore the obvious question is, is the purported increase in violent crime outweighed by other advantages in total social cost? If so, then by his own statements, it's worthwhile.
(Eg, does violent crime then decrease by 5% in the second year?, does the number of petty crimes drop by 50%?, is there an increase in the tax base?, etc.)
Without that, picking out only a single negative is not enough to be actionable.
Also, the data for the paper comes from 1987, 1990, and 1993, and it uses murder rates as a estimate to judge if there are confounding factors. (The paper rightly points out the numbers are based on reported crimes, and not actual crime numbers. It's possible that the report rates go up if, say, black citizens are more likely to report crimes if they feel there won't be a racial bias against them.)
However, the homicide rate in the US in the 1987 was 8.3/100K while in 1990 it was 9.4 and in 1993 it was 9.5. The rate now is half that level. Despite the statistics in the paper, it's impossible to say if the current low level is a direct result of those actions to diversify the police force.
I also think the baseline is rather short, and we have another 30 years of the same sort of data, so it really need to be repeated with a larger data set before I can place any sort of trust in it.