I installed ZDC on Ubuntu Lucid Lynx, and the desktop shortcut doesn't display any icon:

It also read "linux.desktop", and when you double-click it, you get an error message saying the command is unsafe:
I decided to investigate and found out from the properties of this application shortcut that there is indeed an icon listed, but it's not a common icon file, instead it's an icon file with the .icns extension, and it can be found here:
To solve the problem recreate a new desktop shortcut, name it "Zimbra", download this icon and select it from the properties of your desktop shortcut:

If you need the command to open Zimbra, use it with your own username:
"/home/<username>/zimbra/zdesktop/linux/prism/zdclient" -webapp "/home/<username>/zimbra/zdesktop/zdesktop.webapp" -override "/home/<username>/zimbra/zdesktop/zdesktop.webapp/override.ini" -profile "/home/<username>/zimbra/zdesktop/profile"

Please note: There is already a launcher.png file in that folder but it's too small (the icon would look stretched out if used for the desktop icon).