Rated 5 out of 5 stars

I like that add-on. Since I have to use Outlook now businesswise, I wondered, how to get my private CalDAV-Ressource on my machine, without letting it go via the companies exchange server. Lightbird is a nice solution.

Nevertheless, I would like to know how to get it startet without the Thunderbird, which I am not using on this machine?!

This review is for a previous version of the add-on (0.3.3). 

It can't run independently, it's an extension.
You can, however, use SeaMonkey and set it to only open calendar window on start. For a completely standalone calendar there is Sunbird.

Edit: In 0.4 you can do launch Thunderbird with -calendar option to get Lightbird window without the main TB window.