But if I receive an invite in email, when I accept it I am offered only the choice of "Home" and "Recurring".

You need to assign the email address to which the invitation was sent to to the Google Calendar. Open the Calendar tab. In the left pane right-click the Google Calendar - Properties - Email. Select the correct email address from the drop-down menu.

The email address on the invitation and the email address on the Google Calendar properties dialog match. But I can accept the invitation to the Google Calendar.

But I can accept the invitation to the Google Calendar.

Assuming this was supposed to be "can't", you can try to delete the Google Calendar in Thunderbird. Restart Thunderbird, and then re-create the Google Calendar in Thunderbird.

As you suggested, I deleted the subscription to my Google calendar, closed and restarted Thunderbird, and re-subscribed to the calendar. When I click on an emailed meeting invitation (.ics method:request) , I still don't get offered the choice to add it to my Google calendar. And if that's not weird enough, I got an invite to an event(ics method:publish), which only offers the choice of "Add". I can add it to my Google calendar and it appears if I view it via the Google calendar app on my phone, but it does not appear in my Lightning calendar. I can add directly add an event to my Google calendar via the Lightning calendar (ctrl-I, New Event). This appears in my Google calendar and in my Lightning calendar.

How do you access your Google Calendar? Via some sort of add-on, or natively via CalDAV?