"...to an external hard drive..."
What is you Lr version number and Operating system?
And, is the hard drive connected and available to the operating system?
Does the folder specified for the export location have full Read/Write permissions?
Can you provide a screen-clip of the error message?
Are any of the photos in Lightroom shown as 'missing' with the [!] icon on the thumbnail border?
Check your settings in the Export dialog.
At the bottom, in the post-processing section, if the "application" box is blank, make sure the "after export" is set to "do nothing".