No filters applied.
I'll navigate LR to a directory and I'll notice some files are missing (raw, psd, jpg). However, when I go to the directory with Windows Explorer the files are there.
What you see in Lightroom is not a file browser, it will not show you the files if they have not been imported into Lightroom, and it will not show you the files if they have been imported into Lightroom and (probably accidentally) copied into a different folder. Thus it is possible that the results you see in Lightroom are different than what you see in Windows explorer.
I then go back to Lightroom and do a synchronize folder on the directory and the files are not found (synchronize shows zero files to be imported). Any thoughts?
Is it possible that these photos have already been imported into Lightroom and by accident, Lightroom has made a copy (during the import operation) of the photo in a different folder? I think you ought to investigate if this has happened. So, in Lightroom, turn off all filters (Ctrl-L Once or twice), click on All Photographs, select Expand All Stacks, and then search for one of these photos by file name.
Okay, this is bizarre. I went into windows explorer and renamed one of the raw files that weren't showing up in LR. I then sync'd that folder in LR. Not only did it see the newly renamed file, it showed that the file with the original name was now missing. I cancelled that and went back and renamed the missing file back to the original name and again did a sync. This time it shows the file as it should have. At least I now know a work around.
So the most likely explanation is that those photos were indeed imported previously, and accidentally wound up in a folder you didn't expect it to be in.
I'm not sure why your workaround worked, but in any event that's good news.