Thank you. I kind of tagged onto one of the comments. Hope it goes somewhere.
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If the external drive is formatted in the Windows NTFS format then LR can read that format but can't write to it.
You have a couple of options.
1) get a utility for the mac that allows it to write to NTFS formatted drive.
2) If you never plan on using that external on a PC again backup all the files on to another external drive or to the Mac hard drive, Copy the files not Move them. Then format that drive with the Mac OS X format using Disk Utility.
3) If you plan on using that external on bot windows and OS X copy the file on to another drive and format it in the Windows FAT32 or exFAT format.