I think it's a later lens...
My Nickle Elmar is serial 999xx, from 1932, with the "11 o'clock" Infinity lock.
The scale on my lens is in meters and close-focuses to 1 meter. There is just one stop-screw, of the "pillar" variety.
As for the font on the front mount, the "tail" on the letter "t" in Leitz curls around more , and the slashes for decimal point in the stop numbers (eg: 3,5-4,5-6,3-12,5 ) are longer on my lens. Also, the focal length is expressed as " 1:3,5 F=50mm ".
The e-bay lens has the "7 o'clock Infinity Lock" and later style release button, with the concentric ridges, and the focal length is expressed as " 1: 3.5 ", not "3,5"...
My guess is that it is a mid-1930's nickel lens, after the revised Infinity lock. If Leitz rebuilt an earlier lens, they re-used only the glass... the construction of the barrel on the e-bay example is a bit different in several details.
I have no explanation for the lack of a serial number.... mine is plainly stamped in the ring around the front element.
😕