I have CS4 (and now CR5.7) and LR3.2. I just noticed that LR states CR6.2 on its 'about LR' display: yet PS is definitely using CR5.7.
So does PS4 use CR5.7, whilst LR3.2 uses CR6.2?
PS4 doesn't use Camera Raw at all; it's waay too old. Camera Raw didn't yet exist back then. But you don't have PS4 anyway. You have PS CS4 instead.
Lightroom doesn't use Camera Raw either. Instead, it has the same raw engine built in as the respective Camera Raw version has. So the raw engine inside Lightroom 3.2 is the same as the one inside Camera Raw 6.2.
After you updated your copy of Camera Raw to version 5.7, that's what PS CS4 now is using.
Or is LR3.2 forced to use CR5.7 because I have CS4 on my system?
No. Lightroom doesn't use Camera Raw at all.
By the way, you can now download the beta versions (or "release candidates", as Adobe prefers to call them) of Lightroom 3.3, Camera Raw 6.3, and DNG Converter 6.3 from
Adobe Labs. As usual, they support a few new digital cameras and most likely include a few bug fixes. Nothing new beyond that. Most likely, the final releases of these new versions will arrive at the middle or end of November.