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Hard to say if the bust relates to the ring without some side views. The eyes are rather pronounced in each of them, though. Here's another image. It's on this site https://www.laphamsquarterly.org/contributors/lucretius but I don't see any attribution.

Looks like they probably got it from Wikipedia... https://en.m.wikipedia.org/wiki/Lucretius It also shows up here https://www.barnesandnoble.com…choses-lucr-ce/1134766966 Here it says that this image is an engraving from a bust https://www.britannica.com/biography/Lucretius That might be the bust above, but if so it's not a good match to my eye.

There are also lots of images of Epicurus that turn up in a Google search of Lucretius