Just when I thought that the mess between 32 bit and 64 bit was over (I am talking about Linux, of course) I got bumped into it again. Problem this time was the lightning plug-in or add-on for Thunderbird. Here was the solution:
http://releases.mozilla.org/pub/mozilla.org/calendar/lightning/releases/1.0b2rc3/contrib/linux-x86_64/
Me so sad...