This article explains how to install Lightning into Mozilla Thunderbird.
Starting with Thunderbird 38, Lightning is bundled with Thunderbird. This means you don't need to install it separately, but simply confirm to use it once you create a new profile or upgrade from a previous version of Thunderbird.
For previous versions of Thunderbird, the below still applies. The same may be true for Thunderbird 38 for builds distributed by third parties.
The current released version of Lightning always requires the current released version of Mozilla Thunderbird (but older versions of Lightning are available for previous versions of Thunderbird). E.g. as of March 13, 2012, the current version of Thunderbird was Thunderbird 11 and the corresponding current version of Lightning was 1.3 and Lightning 1.2 was for Thunderbird 10 and so on.
You can download the latest released version of Lightning or the latest Development Channel build. The Development Channel build has more features than the latest stable release but might have severe bugs that can cause data loss or crash your application. This build is designed for those testing development builds of Thunderbird
Congratulations, your calendar should now be correctly installed! You find additional information in the Use the Lightning Calendar Add-on article.