But sometimes the drive does not show up in the Folders panel if it does not contain any photos. Then you can't create a folder on the drive from within Lr.
Yes you can: click the plus icon and select "Add Folder...". You are presented with an OS dialogue box from where you can navigate to any drive. Create a new folder on the drive and click "Choose".
The drive and the newly created folder will immediately appear in your LR folder panel.