Oh, Cataclysm is most certainly based on the stock Nexus 6P. Now, the term can have two different meanings... one good, one misleading.
The 'good' meaning. A lot of ROMs will say 'based off stock ROM'. What that means is that the dev actually develops off the software that was released with the phone. That could be anything from the Nexus software to Touchwiz on a Samsung Galaxy S6, or Sense for HTC phones, etc. So the phone will still retain a lot of the look and feel of the untouched phone.... just with some tweaks, customizations or tools.
The other meaning is a ROM that is based on 'stock Android'. Now, what that means, typically, is that the ROM was developed from the Android Open Source Project source code. That's the base source code that ALL Android phones are based on.... some, like Samsung, modify the source a lot, others, like Google's Nexus and the Moto line, tread lightly on the source and just add a few bits here and there, others, like Cyanogenmod, try to pass itself off as a whole new operating system. But it saying your phone runs 'stock Android' just means that the base code hasn't been screwed with all that much.
Things get a little confusing with the Nexus line.... Nexus phones are not 'stock Android'. Technically speaking, no phone runs stock Android because you can't run a phone with stock Android. You need device specific drivers, kernel sources, etc... But a Nexus, or a Moto X, or the AOSP based custom ROMs, they will all have a very similar look and feel as they are all very close to the released AOSP Android source as possible.
As far as what ROMs use what method... they usually call it out pretty clear. If they say AOSP or CM (CyanogenMod), then the ROM is based on the AOSP code.... CyanogenMod is AOSP, just AOSP with a lot of the stuff you need to get it to run on your particular phone already merged into the code base.
Now, as for your LS990, I am not all that sure since I don't really deal with phones other than US English locales. I would assume that the R/L L/R stuff would all be handled by the language packs installed on the phone itself... and I would hope that these locale customizations would be present on not only the factory software from LG, but in any custom ROM anyone built for the phone. But I can't tell you yea or nay since I haven't ever messed with other locales.