How to move (ICSDroid) Calendars to the Phone section
I now solved with installing ownCloud on my server. It was not difficult and is easy to setup. Also it gives the possibility to enable even more features.

So in Thunderbird I just add the online calendar URL to the specific calendar. That's it. The only bad thing is that Thunderbird(Lightning) does not get the colors from the server. So you have to set them manually. 

And on Android you need a special app like CalDAV which is really cheap and as well easy to setup. 

Now you can use any calendar app like the of your Android. Planner Plus or aCalendar. This is totally up to you. I really like Planner Plus somehow.

For me this is a really good solution. Synching is working perfectly even with different users on it at the same time. You can also manage the rights the users have in your ownCloud which was impossible with the row ics Dropbox solution.

I also use the Tasks app of ownCloud, what is called the app OpenTasks under Android, which makes it pretty easy also to use tasks on Android.