How to use it?

Quick check:
1. Do you have the lightning extension also installed?
2. If yes, can you see any events in the calendar tab?

I have thunderbird 45.3.0, and as I understood lightning comes installed with it.

And I have full calendar of events:

http://i.imgur.com/Udg1Q2F.png

If you have thunderbird+lightning+evolution mirror and an the evolution-data-server installed and running (which should be the case since you have evolution installed and setup), there should be no further configuration.

On the first run, the extension will scan the existing agendas in lightning and create mirror events in the default evolution-data-server calendar (also for tasks). From then on, it will only act when an event is created/modified/deleted in lightning.
Note that it does not work both ways. It will only copy events from lightning to evolution. In fact modifying events from evolution might cause some problems.

You can force the first run where everything is copied by changing the setting "extensions.evolutionmirror.firstrun" to "true". You can do this by opening the config editor in thunderbird (see https://support.mozilla.org/en-US/kb/config-editor).

If you still can't see any of the mirror events in evolution, maybe you should check the console for error or warnings (Ctrl+Shift+J to open it).

I forgot to mention I only tested this with Xenial (Ubuntu 16.04) which includes only thunderbird 45.2.0 (previous releases of Ubuntu are fine too).
Can you tell me which distribution you are using? what version of libecal/libedataserver is installed?

"extensions.evolutionmirror.firstrun" was already set to "true".

I also restarted the app an no errors appeared in console.

In the evolution client, should I also I same account as I use for exchange in thunderbird?

I use:
- thunderbird 45.3.0
- fedora 24/gnome 3.20.2
- evolution 3.20.5

How do I tell which libecal/libedataserver I have?

The fact that it stayed at "true" is bad. But at least it is consistent with the events not being synced.
This means that the initialization failed, either it did not find one of the required libraries or it failed connecting to the evolution data server.
Are you sure there was nothing in the console? maybe look under "messages" or "all" ...

>> In the evolution client, should I also I same account as I use for exchange in thunderbird?
No, you should not need to have an account at all on evolution.

For libecal version, try to do "locate libecal" in a terminal.

I will try to setup a Fedora VM when I have some time.

Not sure how errors are logged in in thunderbird, but when I first opened the console there in fact were some errors, but I cleared them and restarted thunderbird (hopping for new errors to show on clean console). And there weren't any errors.

So today I fresh started my pc and thunderbird and I got a bunch of errors:

Could not read chrome manifest 'file:///usr/lib64/thunderbird/chrome.manifest'.

Could not read chrome manifest 'jar:file:///usr/lib64/thunderbird/extensions/%7B972ce4c6-7e08-4474-a285-3208198ce6fd%7D.xpi!/chrome.manifest'.

While creating services from category 'profile-after-change', service for entry 'SpeechDispatcher Speech Synth', contract ID '@mozilla.org/synthspeechdispatcher;1' does not implement nsIObserver.

Timestamp: 20/09/16 10:05:39
Warning: ReferenceError: assignment to undeclared variable ICAL
Source File: resource://calendar/modules/ical.js
Line: 44

Timestamp: 20/09/16 10:05:40
Warning: ReferenceError: reference to undefined property addonFor(...)[aProp]
Source File: resource://gre/modules/addons/XPIProvider.jsm
Line: 7258

Timestamp: 20/09/16 10:05:40
Warning: ReferenceError: reference to undefined property this._environment._currentEnvironment.addons
Source File: resource://gre/modules/TelemetryEnvironment.jsm
Line: 488

Timestamp: 20/09/16 10:05:40
Warning: SyntaxError: octal literals and octal escape sequences are deprecated
Source File: chrome://exquilla/content/exquilla.js
Line: 347, Column: 54
Source Code:
        directory.create(Ci.nsIFile.NORMAL_FILE_TYPE, 0600);

Timestamp: 20/09/16 10:05:41
Warning: Use of Mutation Events is deprecated. Use MutationObserver instead.
Source File: chrome://calendar/content/widgets/calendar-widgets.xml
Line: 495

Timestamp: 20/09/16 10:05:41
Warning: ReferenceError: reference to undefined property "getScriptableHelper"
Source File: resource://interfaces/exchangeBaseItem/mivExchangeBaseItem.js
Line: 1912

Timestamp: 20/09/16 10:05:44
Warning: mutating the [[Prototype]] of an object will cause your code to run very slowly; instead create the object with the correct initial [[Prototype]] value using Object.create
Source File: file:///<email address hidden>/components/nativeComponents.js
Line: 25

Then I see there's an error regarding libecal:

Icallib (Tue Sep 20 2016 10:05:45 GMT+0300 (EEST) ):
 Failed to open libical.so.1: Error: couldn't open library libical.so.1: libical.so.1: cannot open shared object file: No such file or directory

But I actually have it installed (/usr/lib64/libecal-1.2.so.19.0.0)

And then some more bunch of errors:

Timestamp: 20/09/16 10:05:45
Error: TypeError: this.lib is null
Source File: chrome://emirror/content/libical.js
Line: 58

Timestamp: 20/09/16 10:05:46
Warning: ReferenceError: reference to undefined property json._readOnly
Source File: resource://gre/components/nsSearchService.js
Line: 3342

Timestamp: 20/09/16 10:05:46
Warning: ReferenceError: reference to undefined property param.purpose
Source File: resource://gre/components/nsSearchService.js
Line: 1214

Timestamp: 20/09/16 10:05:46
Warning: ReferenceError: assignment to undeclared variable notify_notification_set_timeout
Source File: resource://gre/modules/commonjs/toolkit/loader.js -> resource://jid1-oonoa6xbjznvlq-at-jetpack/lib/linux.js
Line: 221

Timestamp: 20/09/16 10:05:46
Warning: ReferenceError: assignment to undeclared variable retValue
Source File: resource://gre/modules/commonjs/toolkit/loader.js -> resource://jid1-oonoa6xbjznvlq-at-jetpack/lib/linux.js
Line: 246

Timestamp: 20/09/16 10:05:47
Warning: ReferenceError: reference to undefined property timers.push[timer]
Source File: resource://exquilla/ewsUtils.jsm
Line: 64

>> Then I see there's an error regarding libecal:
>>
>> Icallib (Tue Sep 20 2016 10:05:45 GMT+0300 (EEST) ):
>> Failed to open libical.so.1: Error: couldn't open library libical.so.1: libical.so.1: cannot open shared object file: No such file or
>> directory
>>
>> But I actually have it installed (/usr/lib64/libecal-1.2.so.19.0.0)

The error is actually for libical. Can you try to locate this one?

So I have this:

/usr/lib64/libical.so.2

And I assume I would need

libical.so.1, but I can't install it because it conflicts with libical.so.2

Ok so this is the problem.

Can you open a bug saying that we need to fix the compatibility with libical 2.0?

I will try to see what I can do about this.