I use spray on lube for the outsides. For inside necks I use motor mica. When I used an oil based lube for inside necks I would put them back into the walnut media vibrator.
Now I SS media tumble with a Thumler's, spray lube & motor mica the inside necks, size, wipe with clean shop rags and continue with the rest of case prep. I like to use the motor mica, and it works well, because there is no wet lube left inside case necks afterwards. By the time I'm all done handling the cases after all the prep the outsides of them are pretty much lube free as far as I can tell.
Right or wrong I don't do a second tumbling since inside necks are lube free. I detect no ill results from this when I use the final ammo. I think the only downside is that wiping each case after sizing takes time. It takes as much time to wipe clean a single case as it does to motor mica one already outside lubed case and size it. I do a thorough wiping, rubbing with clean shop rag. Maybe someday I'll get tired of that and just re-tumble. Right now I'm just tired of re-tumbling.