The 2a / 3a had several differences, and yours looks like more as a regular II
The two-part lenses were all made prior to 1936, so if it is or was coated, it did not left the factory that way. Actually, I have seen few coated lenses, and most of them are from the final batches.
But, the chromed bezel on the lens, as seen in the photo of your first picture, is a detail with which the lens did not left the factory. So it may very well be that a previous owner tried some enhancements on the kit (but then, why scratch it after going to the trouble of having your lens coated...?)
If the rail has no holes, then it must have been replaced at some time by some careless "repairman"?
Here's a photo I had off-hand that hopefully you can use as reference:
1.- Distance scale for wide angle
2.- The end of that arm ends in a little depression with a line in the middle: aligning this line with a number sets the focusing distance
3.- This rivet engages on the hole for the position of each lens (in the picture, engaged on the wide angle hole)
4.- This is the hole for positioning the arm with the normal lens
5.- Distance scale for the Anticomar normal lens (the black tab with the vertical white line moves to align with the distance when focusing)
6.- Pressure tab to disengage the arm from the holes on the rail, pulling or pushing the front to open or close the camera respectively
Hope this helps !