Sorry you're having trouble creating a new folder within Lightroom, are you on a Mac or Windows?
It sounds like you're working on a Mac.
Please refer to the below link to give read and write access to your external drive within MacOS:
Please let us know if it helps.
Firstly, yes I have a Mac.
I somehow managed to set up new folders. Basically what I'm trying to do is grab all of my image files and archive them in a folder associated with my external drives.
I have two external drives, both of which are connected and listed in the panel on the left hand side. I have tried to click and drag files from the Mac internal drive to those, however the files do not transfer.
I am also aware of the method whereby you would create a parent folder, however each time I right click in the folders a window appears with every option other than to create a parent folder.
It's obviously very simple, however not for me right now... please help.
Have you tried to give permissions to the external drives?