I wouldn't have thought that having LW's downloads saving to an external drive would make any difference. Are you downloading the installer to your external drive as well?

Try changing the location for saving downloads within IE (not LW's downloads, just things that you download from the internet in general). Within IE's options there should be somewhere to change the location of saving downloads.

I don't have a Zune either, so I'm not sure whether the Zune software would interfere with files downloading. You could use Google to see whether other people have run into problems after downloading the latest Zune software.
Is it only LW's installer that you're having trouble with, or have you seen the same error when trying to download other files?

Which OS are you using?