I have never done so nor have I ever been instructed by a manufacturer to do so. However, I've heard that a drop of mineral oil on the threads or down the handle will reduce crud buildup and binding. Can't hurt but I'd avoid the strong smelling oils like WD40 and stick with mineral oil.
I'll lube one when I first receive it, and after a good soaking in dishwashing liquid & hot water. After that, only if it gets gummed up again.
I have an old can of motor weight 3 in 1 Oil that I keep just for the 1 in 20 TTOs that need a lube job. But when they need it, the stuff works, it lasts, and no odor. The current version.
I like to put a half a drop of mineral oil on the threads of my three piece razors just to be extra sure that there will be no corrosion. Necessary, no, easy to do and peace of mind, yes. I swear this is what is keeping the softer aluminum threads on my Ikon Shavecraft like new with the stainless Ikon handle.
I noticed in the Amazon reviews that the red can (normal 3 in 1) contains something that over time might help accumulate grime, whereas the blue can that I have does not. Probably not a concern with razors like it would be with small motors, though.
I too use a drop of mineral oil to lube my vintage adjustables. I also lube the threads of my 3 piece vintage and modern day razors.
Thanks for the tip. I recently bought an "emergency" TTO at Sally Beauty, and the mechanism felt a bit creaky. A little 3-in-1 down the shaft last night, and the turning action is now really smooth.