Have you tried anything?
Like moving your catalog to an internal hard disk to see if you can open it there?
Maybe try moving it to a different external drive (even a thumb drive) and see what happens..
I mean, lotsa people open catalogs on removable storage with Lr5.6, so you might have to try stuff to shake it out..
Why not try to map the external drive to C:/extdrive, and then tell LR to open the library in c:/extdrive? I've successfully done this with DropBox folders, so why shouldn't it work with external drives?