... moving randomly through space, like dust motes in a sunbeam, colliding, hooking together, forming complex structures, breaking apart again, in a ceaseless process of creation and destruction. There is no escape from this process. ... There is no master plan, no divine architect, no intelligent design.
All things, including the species to which you belong, have evolved over vast stretches of time. The evolution is random, though in the case of living organisms, it involves a principle of natural selection. That is, species that are suited to survive and to reproduce successfully, endure, at least for a time; those that are not so well suited, die off quickly. But nothing — from our own species, to the planet on which we live, to the sun that lights our day — lasts forever. Only the atoms are immortal ...
That's not a complete theory of evolution (e.g. there is no inheritance with mutation mentioned) but it is a rather surprisingly detailed version of a modern theory - particularly the choice of words ("intelligent design", "evolution", "principle of natural selection").
(Of course, the translation may be modern, allowing the translator the option of picking modern terminology.)
In the interview, Greenblatt makes no such claim (transcript). A very quick search revealed no sources that don't also come via Krulwich.
Did Lucretius have a passage that can be translated to the above in his works, with provenance prior to Charles Darwin's publication?
p.s. Lucretius also describes atoms, but that is less apparently anachronistic, so it isn't part of this question.