/nitpick
The process of converting fat to soap is saponification, not esterification (or “esterisation”)… 
My WAG is that the lubricant must be food grade, hence eliminating rancid fat.
That’s interesting. I have back fat, the lard from which has become solid but not as solid as the lard I used. It has set nicely and looks to be usable, albeit somewhat soft. It does have a distinct pork odour - the body cavity lard apparently does not.
However, I have a friend who is a butcher. He discards most of the “leaf lard” - that surrounding the organs - and he’s happy to give me as much as I want free (maybe I should start a lard business)
Leaf lard is definitely what you want for cooking - sets up hard, very little “porky” odor, etc. I assume it’s hardness makes it the most suitable for the lubricating task you’re doing as well.
BTW, what’s your rendering technique? I do beef suet in a crock pot/slow cooker (described in that video about 7:00 in) - I just toss it in, turn it to low, cover, stir every few hours, and leave it all day. Works like a charm.
I did exactly this, though on low heat on a gas stove. It’s my first effort, seemed to work out OK.