Here I will describe how you could synchronize your Thunderbird and Lightning with Google Calendar for viewing and creating events on your Android Phone.
1. Preparing Thunderbird and Lightning
For working with events and tasks there is a good add-on called Lightning. So first download and install Lightning through the Add-ons Manager or directly from addons.mozilla.org. Please note to choose the correct version, because for each new version of Thunderbird there is a different version of Lightning.
2. Integrate Google Calendar into Lightning
There are some additional add-ons like “Provider for Google Calendar” but you don't need them for adding your Calendar into Lightning. Google provide a step by step guide. Please click at "Enable Google Calendar in Mozilla Sunbird" (Sunbird is a outdated standalone version of Lightning) and follow the instructions. In the simplest case your Calendar CalDAV URL look like: https://firstname.lastname@example.org/events
3. Adding Events from your Android Phone
Now you can test your configuration. Simply create a new event at your Android Phone Calendar. Select your Google Calendar, enter a Event name and save it with the "Done" Button. If everything goes through the new created event appear in your Thunderbird Lightning Calendar. To speed the testing up, right click your Google Calendar in Thunderbird and select "Synchronize Calendars".
It also works the other way around. So if you create an event in Thunderbird it should appear later at your mobile phone.
4. Optional: defining Google Calendar as default
If you create new events from Thunderbird it will select your local Calendar as default. To avoid this please take a look at this guide: How set default calendar for new events in Lightning?