Well I would lubricate the threads.
What with is the question. Also do it lightly.
I guess the attachment is a steel ring to the Aluminium of the flattener, and as the materials are different there may be preferential lubricants for different mating materials.
I wonder if an oil wiped over the threads by a cloth or tissue would be better. However oil is a liquid and so likely classed as volatile.
Old method was copper grease, these days it seems to be graphite grease. Copper not sure why but the graphite makes sense as graphite is a lubricant itself between surfaces, so even if the carrier grease goes the graphite remains.
The unknown being are either acceptable.
You will get lots of answers. The ones against will be the grease/oil volatiles evaporating on to the lens surface. So expect Yes and No. The point to consider is: Is the use of a strap wrench more or less hazardous then some lubricant.
Really need someone from the high end mechanical engineering side, and not the astronomy side. Too many opinions in astronomy. Any universities around you with a good mechanical Engineering section?
Add a location, someone may know of a good place to approach and ask via email.
Flat81's are rare.