Here are some quick instructions to get your Thunderbird with Lightning to sync up and play nice. Scap a fleet.
Download Lightning to your desktop.
Go to Tools > Add-ons > Install find the Lightning .xpi and install.
Download Provider for Google calendar, save it to desktop.
Repeat above until both are installed.
Log into your Google Calendar, go to Settings, click the Calendars tab and click on the name of the calendar you wish to add to your Thunderbird.
At the bottom, copy the URL of the Private Address from the "XML" button.
Now open Thunderbird. Click the Calendar button on the bottom left, then right click in the left pane. Select "New Calendar," select "On the Network," and click next. Select "Google Calendar" and in the Location field paste the URL of your Private Address that you copied earlier. Select Next, add a name, pick a color, next and finish.
Now that you have this working, you should be able to add tasks/appointments in your Thunderbird/Lightning calendar, and see them in your Google Calendar and vise-versa!
Happy scheduling ;)
Note: When adding tasks in Google Calendar, it might be necessary to click the Reload button on your Lightning calendar to force the update.
Update: If using 64-bit linux, either look in your distro's repo's or try what is mentioned in this thread.