need to move videos from iphoto to Lacie external hard drive
You nailed the problem when you tried to export to your desktop instead of the external drive. It's the export process that's broken.

You could pursue two avenues:


Dig into the video format of one specific file and work through that here. 
Contact Apple support since your version of Photos is likely new enough to get support (or free support on twitter would get you the Apple KB that lists what video formats are supported for export.