The lens corrections aren't part of the firmware itself (i.e. a particular firmware doesn't mean you have a particular lens correction). They are profiles that can be stored in the camera, and you need to register them with the camera if they aren't in the default set.
Canon DSLRs that support lens corrections (Peripheral Illumination and/or Chromatic Aberration) only have space for a certain number of correction profiles. As far as I'm aware all Canon DSLRs that support lens corrections have space for up to 40 lens profiles, but ship with a default selection of about 25 lens profiles.
Note that most Canon DSLR models since about 2008 support in-camera Peripheral Illumination correction (DiG!C 4 or later), while in-camera Chromatic Aberration correction was introduced in models starting around 2012 (DiG!C 5 and up).
I guess these are the profiles Canon deem to be the most likely to be used. The 5D Mark III's default set are most (if not all) of their current L-series lenses (without extenders). This is why the 85mm f/1.2L II is included, but not the 35mm f/2 IS (non-L), and even the older 85mm f/1.2 (version I, no longer available) is not included by default.
In order to add/remove lens profiles, you need to
- connect the camera to your computer via USB
- install & run the Canon EOS Utility,
- select 'Camera Settings/Remote Shooting' mode
- choose 'Lens Aberration Correction' from the lens shooting menu
Here's a more detailed set of instructions from Canon's Support website.
From there you will get an interface to check or uncheck lenses for the camera to remember. Any valid combinations with the 1.4x and 2x extenders are also shown (as separate profiles to the base lens).
It's a relatively simple adjustment, but requires the Canon software and some foresight if you're going to borrow or test out a lens/body/extender.
If you forget to do this in advance, then hopefully you shot RAW photos. You can then use Canon's Lens Aberration correction to apply correction for peripheral illumination, chromatic aberration, color blur, and distortion from within their Digital Photo Professional software after the fact (to RAW files only). For RAW files made using one of 39 lenses with currently available DLO profiles you can use the more comprehensive Digital Lens Optimizer.