If renaming is not possible within Windows Explorer then this directs the blame away from LrC, since LrC merely references files internally, and relies on instructions to the OS for external operations such as renaming - just the same as Window Explorer does.
Perhaps the files concerned are indicated "in use" somehow, or the containing folder. One common issue is if Windows Explorer happens to be clicked onto a file with the Preview pane active. This alone can be sufficient to keep a file 'in use' and so prevent renaming that. More so of course, if the file has just been opened in e.g. PS. Sometimes even if a file's closed within the application, it is not 'released' until that application is fully closed. For example I've found this sometimes with a 'save as': one is now IN the new file, but the old file may not immediately be let go of. Occasionally even, after a glitch of some sort, not until Windows signs out and back in - depending on the particular nature of file system you are connecting to.
Would a file be "in use" even after shutting the computer done (not restart), then starting it? I then open LR and try to sync the folder containg the photos with the same success. I'll be working on some photos today and will attampt to save them from PS the sync folder in LR. Maybe that will shed some light.