The following steps need to be followed to enable Thunderbird you use your calendar at Google Calendar. The assumptions are: Thunderbird is installed with the Lightning Add-on, and you have a Google account and can access Google Calendar.
1. Open Thunderbird. Click on (in the menu) Go->Calendar (Ctrl+3).
2. Click (in the menu): Calendar->New Calendar. A new window will be open which asks you
to create a new calendar.
3. Select "On the Network" and Click "Next"
4. Select CalDav and in the Location Field enter:
https://www.google.com/calendar/dav/ [ your Google Calendar ID ] /events
For your primary calendar your Google Calendar ID is your email address: For example,
5. Assign it a name and other properties you wish to assign.
6. Once this is done, you will be prompted for your google id and password.
Voila!!! You can now synchronize your Google Calendar with Thunderbird. To check it add an event in Google Calendar from your web browser and see if that event shows up in Thunderbird and vice-versa. It will work, but I would advise you to try it.