Rated 5 out of 5 stars

Sync Kolab still works pretty well and is the only tool that I found so far, that can sync all your Lightning and Contacts data to YOUR OWN imap folder.
(Of course there are other plugins that can sync stuff, but they only sync your data to THEIR servers, so they can harvest your data.)

Now, since it seems some people have difficulties getting started here, let me give a quick introduction.

1. Open the Thunderbird AddOn page in Firefox and download Sync Kolab to your computer.
Since the author has not given his go for the new TB version, TB thinks Sync Kolab
does not work with the current TB Version, but it does.
2. Start Thunderbird, go to AddOns, klick on the little cogwheel symbol and select
"Install AddOn from file" (or what ever it says in your language).
Select the downloaded addon and install it.
3. Restart TB.

HINT: Before you start step 4. create a subfolder called "Sync" within the emailaccount (aka IMAP folder) that you want to use for storing your sync data. If you want, also create subfolders therein called "Contacts", "Tasks" and what ever items you want to sync. Following this hint may not be necessary, but I highly recommend this to keep things sorted.
While you are at it, make sure your email provider does not automatically delete old messages within those folders.

4. Go to the AddOns page of TB again, select Sync Kolab and click on "Setup" or "Settings" (depending on your language).
5. In the SK menu, on the left, you can see your emailaccounts. Select the entry "Contacts" under the emailaccount, within which you created that "Sync" folder earlier.
Now click on "New" below to create a new synchronisation job.
Then enter a name for that synchronisation job, like "SyncMyContacts".
On the upper right you can now see your addressbooks and on the lower right you can see the folders of the selected emailaccount.
First select the addressbook you want to synchronise (like "Private Addressbook"), in the upper right.
Then navigate to your "Sync" folder and click on it to select it, in the lower right.
Don't click anywhere else for now, just click OK (the reason being, clicking within the menus to the lower left and right , selects items and hence changes the configuration).
(You can do the configuration for all your sync tasks at once, but doing more clicks than necessary results in potentially unwanted configurations.)
6. Repeat step 5 for every addressbook, calendar or other stuff you want to synchronise.
7. Rightclick on your TB toolbar and select "adjust" (depending on your language). Then draw the "Sync Kolab" button into your toolbar.
8. Klick on the Sync Kolab button, to start your first synchronisation.