I got this to work, and here's how I did it:
I use Thunderbird/Lightning as my email/calendar client on my main computer (Thinkpad W541, Ubuntu Unity, 16.04) and my travel Chromebook (Acer C720, Ubuntu XFCE, 16.04), and I wanted to regularly sync the calendar data between both machines. Suggestions online often mention Google Calendar, but I'd rather use open-source tools (that I control) to do the job. I use SeaFile (a FOSS DropBox equivalent) to sync folders & files between my machines.
Step 1: On my new Chromebook, I copy over my entire Thunderbird directory:
rsync -zarv user@thinkpad:~/.thunderbird/ ~/.thunderbird/
Then, I install Thunderbird and open it: presto, all my accounts, old emails, and (most importantly) calendar events are accessible. Great!
Step 2: It looks like all relevant Thunderbird data are stored in ~/.thunderbird/blah.default/, with calendar data in ~/.thunderbird/blah.default/calendar-data/. On the Chromebook, I create a new calendar event, save it, and see that ~/.thunderbird/blah.default/calendar-data/local.sqlite has increased in size and has a newer "last-modified" timestamp. I conclude that local.sqlite contains all relevant calendar data.
Step 3: I close Thunderbird on both machines, then use SeaFile to sync the entire calander-data/ folder on both. I see that the newer filesize and timestamp have successfully synced on the Thinkpad. I open Thunderbird on the new machine, and there in the calendar is my new event. Success!
Drawbacks:
The main drawback seems to be that if Thunderbird is open on both machines and either calendar is edited, syncing the calendar-data files sometimes causes the other machine's Thunderbird to crash. They just weren't built to handle that sort of I/O. But otherwise: it works great!