If we agree, and by LENR you mean "a collection of apparent excess heat phenomena within chemical + experimental error bounds, but not understand at the time" - then yes. LENR is timeless and sightings no doubt go back to the 16th century.
This seems like is a suitable understanding of LENR for the present discussion. By this understanding, I don't think LENR would be something that would have been discernable as a phenomenon until the awareness arose that there are nuclei and that different processes occur with them, as well as the invention of electricity and calorimetry and possibly radiation detection. So around around the start of the 1900s. Do you agree?
If, OTOH, you mean by LENR: "credible evidence for extraordinary excess heat from nuclear reactions" the problem is that in the dim and distant past, before anything was understood of NAEs and the rest, such old sightings would be less well documented and therefore even less credible than modern sightings.
For the reasons mentioned above, I don't think we can go into the distant past.
Inevitably, for a real phenomena with physical basis, with continued attention and collection of evidence, the phenomena will become, sharper, more reproducible, more understood. By far the best evidence will be recent. Which is why I see the historical bent of much LENR community discussion as profoundly negative.
With respect, this seems like one of those easy generalizations of scientific progress that Feyerabend sought to address. I'd argue that what we're looking at is a subfield in a very early stage, before normal science has taken over, and that people are still fumbling around to a certain extent. That happened with the discovery of chemistry and of radiation as well. This forum has focused on the NiH system because Andrea Rossi has brought a lot of attention to the field. That system is less understood than the PdD system, so things are in an Edisonian mode of exploration. And there are a lot of hobbyists (like myself) who do not feel fully committed to the methods of normal science in the present context, which makes things even more Edisonian than they otherwise would have been.