Let's start with Campbell Law School professor Lee's essay.
Titled "The Firearm and the 'Culture of Death': Foundational Presuppositions and Fundamental Questions," Lee summarizes his argument as follows:
The Catholic Bishops have renewed their concern over the role of firearms in forming a “culture of death” in contemporary America. This essay considers what is demanded by a consistent understanding of the Culture of Life/Culture of Death distinction that John Paul II developed in Evangelium Vitae. It suggests that the right to keep and bear arms comes with substantial responsibilities. It concludes that the regulation of firearm possession and use must be a part of any decent legal system, since firearms are potentially destructive not only for the victims of firearm violence, but also for persons who use them and for the culture in which they are present. The good of the victim of gun violence, the gun owner, and the society as a whole must be considered in determining morally appropriate firearm policies.Regent professor Louis Hensler
counters with a close reading of the relevant encyclical and observes that the Pope used the expression "culture of death" in a specific way: "John Paul focuses his attention on a particular form of attack on life: attacks affecting life at its most vulnerable, earliest and final stages. John Paul writes of abortion and euthanasia." In other words, simply draping one's position with the mantle "culture of death" does an injustice to John Paul's deeply analytic consideration of a narrow set of phenomena.
That John Paul's encyclical does not address gun violence does not, of course, render his analysis of abortion and euthanasia irrelevant. It does, however, suggest that much more work needs to be done before applying the label "culture of death" to activities--gun manufacture and ownership--that do not, in themselves, cause anyone's death.
The immediate object of abortion is the death of the unborn. The immediate objects of guns are manifold. Some objects of gun manufacture and certainly gun ownership are indeed illicit but many are not. Labeling an activity "culture of death" may be evocative but in itself lacks the kind of analysis necessary to persuade.