In the current version (0.18 with lightning 1.9.1), this is a hidden feature which is disabled by default. It is slightly buggy, but works sufficiently to just get an invitation into your google calendar from your (possibly non-google) inbox.

Using the config editor, simply set calendar.google.enableEmailInvitations to true. You may also want to set calendar.google.sendEventNotifications to false to avoid the possibility of an old bug that sent new events instead of notifications; I've not tested this. Then, restart thunderbird.

Once you have done this, in the properties of your google calendar, you will have the option to associate it with an account.

If it still does not work, try deleting and reconnecting your calendar via the xml-address from the Google Calendar website.

After you do that, you will get the appropriate buttons (they will appear with a brief delay as your google calendar is checked to see if the event exists). If it doesn't, you can use the accept/decline/tentative buttons as with other calendar types.

One bug that currently exists is that if the event is in your calendar already, you will get an update button whether there is any change or not. The button will usually cause an error if pushed.