Kroysa - Stephan van den Zegel has at least one Sonnar that shows similar knurling to the lens in the second eBay listing. Whether these are "authentic factory production" or not will never be known.
Several folks, including myself, have speculated that there was cottage industry that may have started before the end of the war and continued into the post-war period where some unknown more-or-less skilled craftsmen hand-built a number of "Jena" lenses, probably in order to raise hard currency. I suspect that as things got dire for the Reich, some components may have left the Jena factory in empty lunch kits.
These lenses were NOT Jupiter-3's with faked trim rings. I owned one of these LTM lenses - the optical module was not Russian, nor was it a Jena factory product - it looked for all the world like a hand-machined and rather roughly finished all-alloy barrel (rather than brass). The serial number was not listed in Thiele. Brian Sweeney has this lens now. I also had a Contax-mount 50/1.5 Sonnar from the same period that was listed in Thiele, but had a somewhat roughly finished brass mount shell and a well done alloy optical module, except for the rear triplet assembly which was made of brass and stamped with the serial number matching the trim ring.
I think these oddball Sonnars are fascinating, and I wish I knew the real story behind each one of them. They have collector value to some, and this is reflected in the asking prices. I would not buy one of them expecting excellent or even adequate optical performance. If you want to USE a Jena Sonnar in LTM, get one of Brian's hybrids.
Or buy an authentic Contax-mount Sonnar (for the optics) and a decent-looking J-3 (for the mount) and build your own -
Brian has posted good instructions. I have made a couple myself following these instructions, though I don't have a nifty through-the-lens viewer; I use the actual body I'm going to mount the lens on to set infinity, and the R-D1 to shim the optics for close-focus.