How do I sync Thunderbird across two computers?

Just sync the whole profile folder over Dropbox.

You can set your thunderbird profile up on a (large) memory stick and then just take it with you. You'd probably want backups and some sort of encryption in case it gets lost, though.

The other idea would be a Dropbox folder, if you can install Dropbox on your work laptop. Since you got Thunderbird installed, I assume you're allowed to at least install software. The firewall may be another issue.

The only suggestions and utilities online deal with sneaker-net methods (portable drive profile above) and network drive methods (Dropbox or LAN/WAN).

UPDATE response to dropbox clarification question:

I assume you're familiar with cloud storage systems such as Sugar, Dropbox, and the like. Most of them result in a particular folder or folders being copied from your computer to cloud storage "out there". Installing the host program allows you to keep files on multiple computers synchronized pretty effectively as well as backed up on the cloud.

You would set up Thunderbird to store it's profile data in a folder that Dropbox (or whichever app you choose) backs up and synchronizes.

Then you set up the Dropbox client on your work computer and download that same Thunderbird profile data to that computer.

Technically, using the portable version of Thunderbird, you could put the app itself in the cloud storage so it could be accessible wherever you download it.

All updates and changes would then be synced between any systems you have the the dropbox client and thunderbird app set up and configured properly.

Another solution, which I use for non-syncing apps,

would be symbolically linking (scriptable, cross-platform)

certain files (filter *.dat file, etc)

from a Resilio Sync folder (free, self-hosted, infinite space) a la Dropbox.

Using this method you cannot open it on both computers.

As for syncing mail, DO NOT BOTHER WITH THIS MANUALLY. Just switch to an IMAP mail server and THIS IS DONE FOR YOU. (Don't use POP)

As for Calendar, THIS IS DONE FOR YOU, just use Cal-DAV (Google Cal, or OwnCloud for self-hosted)

As for Contacts, THIS IS DONE FOR YOU, just use CardDAV (Owncloud)