I think maybe my question wasn't clear enough. On my camera (as on most) there is a dial that sets the white balance. It has a setting for "shade" a setting for "tungsten" a setting for "auto", etc. When I look at my photos in LR, I'd like to know what that dial was set to so that I can learn from what I liked and what I didn't like so that I can get more pictures 'right' directly out of the camera. Can LR do this (display the WB setting info from the camera)?
As far as I know, no, LR can't tell you what the textual preset was.
You can, however, see the exact colour temperature and tint used, which may teach you a bit more about how those temperatures work.
If you want to see which textual preset was used in the camera, this information may be stored in the EXIF headers, if your camera does that. Depending on which operating system you use, there are a number of tools that can do this job for you (list the complete EXIF headers).
I downloaded and installed
EXIFutils for my Mac. The software apparently works with Windows, too.