The birthday addon you mention seems to extract birthdays from all contact info in address books. Info says: a birthday calendar is automatically created for each address book you have. It does not mention anything to do with synchronising anything with the google Birthdays calendar.

You have to use the google Birthday calendar if you want birthdays reflected in google.

• Click on 'New Calendar'
• Select 'On the Network' and click on 'Next'
• User name - enter gmail email address
• click on 'Find Calendars'
• It should list available calendars and one of them should be called 'Birthdays'
• Select 'Birthdays' and click on 'Subscribe'

If you really need an answer on whether that addon can synchronise with a google bithday calendar then perhaps you should be talking to the author of the addon extension. At this link: https://addons.thunderbird.net/en-us/thunderbird/addon/birthday-calendar/ you will find a 'Support Email' link.

Thanks Toad-Hall, I've contacted 'Birthday Calendar' extension author as suggested. I continue to struggle to understand the details of the link between 'Lightning' and 'Google Calendar'. All my established calendars seem to have excellent two-way communication (e.g., changes in either calendar are reflected in the other), while the (internally generated) Birthday Calendar does not. Puzzling. I do note that Birthday Calendar displays perfectly within 'Lightning', but is 'tagged' with a 'locked' icon. Attempts to remove the 'read only' status are unsuccessful. Nevertheless, even as 'read only', it would seem that Google Calendar should be able to reach out and 'read' the file. Anyway, although this remains unresolved, I'll mark this as 'solved' and move on with life. Thanks again.