The instructions posted by @ChuckPa in his reply describe the “correct” way to add a NTFS-drive to your Linux system with correct permissions. Unfortunately, it is not as easy as plugging your drive into your Pi and letting the desktop environment (LXDE) handle things for you. LXDE just makes sure the logged-in user (pi) can access everything and does not care about anybody else.
Please let us try the hard way (temporary), just to show you the instructions would work:
(1) get the device name for your extern drive: mount | grep "/media/pi/ledisk". We are looking for /dev/sdb1 or something like that.
(2) unmount your drive sudo umount /media/pi/ledisk
(3) create a directory in /mnt we will use to mount your drive at: sudo mkdir /mnt/ledisk
(4) mount your drive with default options at /mnt/ledisk, assuming your external drive is /dev/sdb1:
sudo mount -t ntfs-3g /dev/sdb1 /mnt/ledisk
(5) try to access this directory in Plex
In theory, this should to the trick, temporarily. Afterwards, we have to add an appropriate entry to /etc/fstab to make this permanent.
I can do some experiments with my Pis later this week to find a more “accessible” way to have Plex up and running within seconds.
Btw: you might not be aware of the official Plex Ubuntu Appliance. It’s Ubuntu preinstalled with Plex and supported by Ubuntu. https://ubuntu.com/appliance/plex/raspberry-pi . If there is nothing else on your Pi right now and starting from scratch is an option for you, you could also try this Appliance.