I’m happy to announce that Lightning 1.1 has been released. If you were having trouble with alarms then you will want to upgrade to Thunderbird 9 (or Seamonkey 2.6) and Lightning 1.1.
If you are experiencing issues (Lightning not installing or the calendar not working at all), I’d suggest uninstalling Lightning and then doing a fresh install. Your calendar data will be kept intact, as it is contained in your profile.
You can get the builds on addons.mozilla.org, as always.