Saint Augustine says that lust is needed to copulate and that all sex acts perpetuate sin
First, this isn’t true–he is not so sweeping. Second, what he says, and say, what St. John Paul II teaches in his Theology of the Body audiences are not really all that different.
St. Augustine, in opposing the Manicheans, teaches the desire is good–like the desire to eat–because it leads to the sustaining of the human race, like eating leads to the sustaining of the individual–and both are pleasurable to encourage this. He said those acts done solely for pleasure and not open to propagation are done by lust (and then only venially). He uses the analogy of eating both temperately and intemperately.
JPII’s Theology of the Body also discusses the possibility of the sin of lust, even in marriage. Sexual desire strictly for pleasure is still considered lust, just as eating strictly for pleasure is gluttony.
Both Augustine and JPII agree that even marital relations can be tainted from the “intemperate carnal lust” (JPII’s words), but both agree that this evil can in principle be separated from the act, and that this does not make the object of the lust itself evil (ie only the lust is evil).
Where they differ is St. Augustine had a more pessimistic view of man’s ability to separate them due to his fallen nature than other theologians and moralists (but he was not alone in his view either). And while we may have a more optimistic view than St. Augustine, even St. John Paul II warns that we need be mindful of the “call to dominate the lust of the flesh.” And both are clear that this call is not to denigrate marriage, like the Manicheans said, but to preserve its dignity.
See e.g here for JPII (sorry, can’t seem to find it on english online, but here is the Spanish which runs well through google translate):
http://www.vatican.va/content/john-paul-ii/es/audiences/1980/documents/hf_jp-ii_aud_19801022.html
And Augustine:
https://www.newadvent.org/fathers/1309.htm