Open the Add-ons Manager and disable Lightning.

Thank you, that was a surprisingly easy solution. When I saw "packaged with", I didn't expect a shipped-with plugin. I figured the Lightning code had been folded into the main Thunderbird codebase and there was a preference somewhere I was missing.

Per the main Thunderbird support page, "Starting with Thunderbird 38, Lightning has been packaged with Thunderbird.". Any idea why it suddenly start nagging me about events in 52.4.0, over two years later?

Any idea why it suddenly start nagging me about events in 52.4.0, over two years later?

You haven't really provided a wealth of information about the problem. Based on what you provided:

Thunderbird has started giving me notices: "This message contains an invitation to an event."

Assuming this is what's 'nagging' you, I'd say you received a message containing an invitation to an event. Whether you received such invitations before I don't know. In any case, I may be completely wrong with this.

The nominal invitation is an email I wrote, which I'm on the CC: list for. It contains no invitation. That email is part of a longer email discussion. The part which I added -- which triggered the notice -- is "Was there ever an agreed-on time for a reboot of horntail?". There are several other messages in the chain that also referred to time, which did not trigger the notice.

I've received several actual event invitations before this -- spam for webinars, for example (which was not recognized as spam by Thunderbird) -- none of which triggered the notice. Thus my puzzlement, and thinking this was new behavior in Thunderbird.