Lightning is a calender extension for Thunderbird. Thunderbird has built-in support for searching and installing add-ons. But unfortunately this search function does not find lightning for 64 bit Ubuntu.
One way of installing the extension is to find a 64 bit compiled extension in Mozillas archives. But the archives seems to have a lack of files with precompiled 64 bit versions for Linux.
I found out that the easiest way to install Lightning on a 64 bit Ubuntu (in this case Ubuntu 11.10) is to install it with apt-get. Install it by running this command:
sudo apt-get install xul-ext-lightning
When you start Thunderbird the next time Lightning will show up!
