Make sure you have read and write access on this external drive.
Did you recently used this external drive on a windows machine for some other purpose.
How is the drive formatted, Windows NTFS or Mac Extended (Journaled)?
Did you recently upgrade to OS X El Capitan?
Did you have a Utility to Write to Windows NTFS formatted drives?
More than likely that drive is formatted in the Windows NTFS format and you did have a utility that allowed Mac OS X the ability to Write to that type of format and now you have upgraded OS X to El Capitan which removed or disabled that utility. Leaving you without a way to write file to a NTFS formatted drive.
Yes I have upgraded to the latest release of OSX, I did not use this drive on a windows machine, please note that I am able to read/write into this drive from my mac using finder, only when I try to export the pictures using adobe I see this problem. Again, I am able to both read/write on this drive using my mac and I see the folder structure just fine, only when it comes to import/export using lightroom, this problem occurs.See finder view of folder structure in screenshot.
See below answer.
Right click on the drive, then click on get info.
Scroll down to permissions and change it to read and write for everyone, apply it to all.
Now check with Lightroom if the issue is resolved
You had a utility that allowed OS X to both Read and Write to that format. You have a couple of options.
1) Get another utility or an update to the one you had that works with El Capitan.
2) Copy, Not Move, everything off that drive then format it in the Mac OS X format then copy or move everything back on that drive.
There is no way to set any permissions on that drive. OS X can not write to NTFS formatted drives natively. It can only read from them. Since you can write to it you can't change permissions.
NOTE that 99.99999% of all external drives sold are Pre-formatted in the windows NTFS format as it is the predominant format of all computers sold for the last 15 years.
So in the future when you buy a new external drive the first thing you do is change the formatting to the Mac OS X format. That way you won't run into this problem again.
This fixed the problem for me :
For anyone using Seagate drives, I heard back from Seagate tech support and there is new driver software available here:
After I installed the new Paragon driver - everything works for me now. I have read/write access again.
You will until Apple updates El Capitan or comes out with a completely new version of OS X that will once again Remove that utility/Driver and you are back to not being able to write to that drive.
Honestly if you are using a Mac the external drives you connect to that Mac should be formatted to work with OS X without having to install or update some Driver/Utility.