First of all, assuming we are talking about lenses on Rolleiflex twin-lens cameras:
After the war, "Operation Paperclip" by the US forces literally forced a number of Carl Zeiss staff members from Jena to the American zone (along with substantial equipment) so as to establish a new Carl Zeiss operation there, knowing that Jena would have to be handed over to Soviet administration. At first this new firm could not use the Carl Zeiss name when the right of use was still very much up in the air, so all its products were marked Zeiss-Opton, until 1954.
I have a 1951 model Rolleiflex with a Zeiss-Opton Tessar, and found it to be quite unuseable at first; after examining its construction, and communications with fellow collectors, it seemed obvious that, at least for some of the lenses supplied to Rollei and the new Zeiss Ikon in Stuttgart (formerly Contessa-Nettel), the lens cells by Zeiss-Opton were badly designed to the point of being appalling, to the point that, after a few decades, the lens can deteriate to the point of not being able to produce an image.
The Tessar design consists of four elements in three groups, two air-spaced single elements before the diaphragm (in this case, shutter as well) and a cemented doublet behind it. Like any lens cell, the groups have to be held securely, and Jena, no matter pre or post war, did a good job. But the Zeiss-Opton version of this lens, the groups were not even mechanically supported and spaced correctly.
The rear group should really be dropped into a cell, and its edge either turned to lock it in position, or a locking ring screwed in to secure it. But in this case, the rear group was dropped in and glue was squirted around it. After a period the glue moved, and the inner element, while still attached to the outer element, slipped out of alignment, causing severe decentration of the whole system, and at the same time, the whole group also slipped out of its cell.
At the front, the normal way is to have the two elements spun into its own cells and then screwed together, or the inner element spun into the end of a longer cell "tub", the larger front element dropped in, and then a locking ring screwed in from the front. But in this case, while the front element was held in position by a locking ring (which makes it looks very secure) the inner element was again held by glue which moved after a number of years, completely upsetting the optical configuration.
It took me a fair while and some extensive work to get the lens back into working order again, the cost was not insubstantial; so in that sense it put me off Zeiss-Opton!
But back to the original question:
Generally speaking, pre-war Rollei twin-lens cameras use four-element Tessar and three-element Triotar lenses; after the war it switched supplier to the new Zeiss firm in Oberkochen who supplied Tessars which are optically good but likely to be mechanically inferior than pre-war ones, until about 1954. For the Automat and the T-series, Rollei used four-element lenses of f/3.5 maximum aperture, and for the more advanced models, five-element lenses of either f/3.5 or f/2.8 maximum apertures, and those are Planars and Schneider Xenotars. The first 2.8 (model A) used a very stretched Zeiss-Opton four-element Tessar and it was not satisfactory, so for the model B Rollei returned to Jena to get its Biometar which is, in design and construction, the same as the Xenotar. It was only from the model C onwards that Rollei used either Planar and Xenotar f/2.8, depending on whether Zeiss or Schneider had them ex-stock ready for delivery on the day.
Being the "junior model", the Rolleicord first use three-element Triotars but after the war it matured dramatically and upgraded to using Schneider Xenar four-element lens, which is also a worthy performer.
