Synchronization of Google Calendar with Mozilla Thunderbird Lightening works as a charm. Install Lightening, which is an add-on for Mozilla, for the calendar part. But this will not give a bi-directional access for Google Calendar. So, you need to install one more add-on called Provider for Google Calendar. Set up proxy server in case your network requires the same else nothing to do with the preferences.
I have set-up CalDAV as per below,
1. Open the Lightening application and Calendar > New Calendar.
2. Select On the Network and click Next.
3. In the format option select the CalDAV option.
4. In the Location field, enter [ https://www.google.com/calendar/dav/ [ your Google Calendar ID ] /events ] and click Next. eg. [https://email@example.com/events]. Be sure to use https in your URL, as an http address will not work.
5. Enter a name and select a color for your calendar.
Click on the Reload icon/button. A pop up screen will be shown for entering the user name/password. User name consists of the whole email address, eg. firstname.lastname@example.org. Enter the password and you are able to see the sync between the two calendar’s.