An ingredient of Japanese washi paper is a gloopy substance called neri extracted from abelmoschus manihot (or tororo-aoi, even though it has no relation to yam) roots. It's unknown if it was ever used as lube.

It's plausible that if a thing is remotely cylindrical, someone will attempt to insert it somewhere; and if a thing has a hole in it, someone will attempt to insert themself into it. There are many ER docs and nurses who can attest to that. >.>

So, do I think animal grease as lube has probably been done? Yes. But there are considerable downsides. First, as you pointed out, they're much more likely to go rancid quickly. (Vegetable oils will also go rancid, but not usually as fast.) Then there's the fact that most of them are going to be solid at room temperature and would require warming to be used. That's not necessarily going to stop anyone, but it does put a throttle on the action. And then there's the issue of odor. YMMV, but I don't particularly fancy the thought of smelling like bacon. {= P

There might also be religious or other social barriers to using at least some animal fats. Pork and beef spring to mind as likely to be taboo in some cultures.

It might be better to reach for butter, particularly clarified butter/ghee. It's more shelf-stable than regular butter and other animal fats, and has a less potentially offensive smell. (Ghee reminds me of popcorn butter more than regular butter.) Also, any culture that has domesticated herd animals probably has butter. At the least, I know you can make goat-milk butter. Dunno why you couldn't also make sheep butter, camel butter, horse butter, or butter from whatever else you may choose to milk. (I have now used the word "butter" enough times that is has lost all meaning and looks really, really weird.)

I wonder if all of this is more likely in northern climates, where there aren't as many options for plant oil/mucilage. Off the top of my head, there's flax in Europe and slippery-elm trees in North America? But flaxseed (a.k.a. linseed) oil is a) difficult to process, and b) not very stable, and I don't know the first thing about slippery-elm bark except that it has its name for a reason and is used medicinally as a throat soother. More research needed.

And I might even do it, because having a list of plausible lubes to offset all the dubious lubes seems like a good idea!

~Neshomeh