Can you show us a screen capture of the Lightroom Import dialog box, and another screen capture of the external HD as it appears in your operating system?
Also, please state the exact version number of Lightroom and what operating system you have with exact version number.
Lightroom's Library Module is not a file browser. Folder don't just show up in Lightroom's Library Module because they exist in your operating system, they show up only when at least one photo in that folder has been imported into Lightroom.
You earlier said
I have been trying to copying photos onto my external hard drive and then importing them into LR library.
In the Import dialog box, you should be able to import from any folder on any disk, the import dialog box operates differently than the Library Module.