Does Lightroom or Photoshop display the AF Fine Tune setting used in a Nikon DSLR in some panel? I need this information when I'm viewing the images that I use for focus testing and adjustment. Nikon's own software (ViewNX-i and Capture NX-D as well as their predecessors do display this information but are prone to frequent crashing).
No, the information is not displayed.
The information you are looking for is in the "MakerNotes" section of the EXIF data. None of Adobe's products read this section.
ExifTool will show you everything in the EXIF data. (Get the mac or window utility, not the Perl library.)