Apparently you've tried to install it in Firefox, not Thunderbird. Try installing it from the Add-ons Manager in Thunderbird itself, or download the XPI file using Firefox and then drag-and-drop it into Thunderbird to install it there.

Lightning 3.5b1 is the version for the beta version of Thunderbird you are using. As mentioned above it will work better if you install it into Thunderbird and not Firefox. There is never a version that works with Firefox.

He is using Firefox 33.0, there is no indication which Thunderbird version he wants to installing it to (assuming current 31.2.0 release, no beta required).

You are correct. I need to stop answering until I have a little more coffee and my reading skills improve. :)

Thank you both. I did as suggested and finally got the Calendar installed in Thunderbird. It is working just fine. I have only been experimenting with Ubuntu and the associated programs for about 6 months now in order to know how to program and use it all, so I can ultimately drop Windows in the near future. I am still learning how to install programs with Linux. Again thank you and if I may ever be of help, let me know.

You are welcome. If you want to help here, it's fairly straight-forward. Just browse for any problems where you think you can contribute (e.g., for Thunderbird, use https://support.mozilla.org/en-US/questions/thunderbird?owner=all&show=all to get the list, sorted by age of their last posts) and comment there.