Overview
Google allows a Google Calendar account to synchronize via the CalDAV service. To add a Google Calendar account using Generic CalDAV perform the following stepssteps:

Select Accounts > Add New online Account > Generic CalDAV.
On the CalDAV screen:
Enter the full email address in the Username fields.
Enter the password used to access Google Calendar in the Password field.
In the Server Address field, enter https://www.google.com/calendar/dav/<emailaddress>/events where <emailaddress> is the Google email address.
Click Save.

I got the commands from the instructions on setting up Anbox.

I'm not 100% sure but I think anbox is more deeply integrated that in fact it has to be in the real rootfs and wouldn't work when installed in a libertine container.
Besides that, anbox is early alpha, so I wouldn't take things necessary there as a pattern/template to do more standard things.
Once anbox is stable - whenever that might be - all the tampering with the rootfs wouldn't be needed anymore.

I'm surprised syncevolution didn't work, I recall reading about it on the forum, although I didn't test it.

Regarding it not being "undone" after the terminal is closed, yes, I see in these instructions that they do specify explicitly remounting as "ro" before exiting (at least in the "Troubleshooting" section, though odd that the command wasn't included in the prior sections). So yes, best to include this. As you say, best probably to stick with Libertine (though given its failure, at least on my phone, to run GUI applications, I sorta forgot about it). [edited to add] I tried to install a command-line program on Libertine, and there's no way that I can see to run it. Libertine seems to be exclusively for GUI programs.

Anyway, I'm guessing that given the instructions for Anbox (which does involve installing from APT) that installing a small command-line program can't be any more harmful, provided the system is returned to read-only status. Regardless, I did update my comment above to (a) make sure read-only status was returned to and (b) to include a warning based upon your feedback.

The best way to install packages from the Ubuntu archives on your device is with Libertine: https://docs.ubports.com/en/latest/userguide/dailyuse/libertine.html

Command-line Linux programs work on Ubuntu Touch. So, a possible solution would be to install something like calcurse (it's available as a package) on both your Ubuntu phone and (presumably) Ubuntu desktop. Then simply "sync" by replacing the "todo" and "apts" files, via a file manager, as needed (IE, whenever one of these files has been altered on either the phone or desktop). These files are located in the following directory of both the phone and the desktop: ~/.calcurse

To install it, run the following from your desktop while your phone is plugged in via USB:

mark@debian:~$ adb shell
* daemon not running; starting now at tcp:5037
* daemon started successfully
phablet@ubuntu-phablet:~$ sudo mount -o remount,rw /
[sudo] password for phablet: 
phablet@ubuntu-phablet:~$

phablet@ubuntu-phablet:~$ sudo apt update

phablet@ubuntu-phablet:~$ sudo apt install calcurse

phablet@ubuntu-phablet:~$ sudo mount -o ro,remount /

And that should install it. The last command is to leave the system as read only (ro), which I gather is important. I obtained the commands to allow for usage of APT from the description on installing Anbox (see here: https://docs.ubports.com/en/latest/userguide/dailyuse/anbox.html)

Afterthoughts:

If you don't mind command-line programs, the following are ones that I find useful.
Midnight Commander (known as "mc") is a recommended command-line file manager. Also, "locate", which helps with finding files after running "sudo updatedb", is also a useful command-line program.

[edit]
Well, the stuff below about "SyncEvolution" was wrong. Not a solution.
[/edit]

I notice that Evolution has its own syncing program, called SyncEvolution, which is described as being able to, "Sync personal information data using SyncML and CalDAV/CardDAV (CLI)".

1.) Ubuntu package for SyncEvolution
2.) Homepage of SyncEvolution

Well, I'll give this a try, but I doubt it will work. Likely, as others have said, some sort of "Cloud" service needs to be set up (though I've tried using the localhost on my desktop in the past to set up some sorta syncing thing, and that failed).

Alfred Neumayer's app GhostCloud makes interacting and downloading files from NextCloud much easier than it used to be, but I agree with you and others: closer integration with NextCloud would be really good.

thank your for sharing your experience. I made similar experience as Kalle and I get a bit upset when the easiest things become something impossible in this world.

Anyway, I will make some effort to get this done and would let you know about the results. But don't expect much because I'm not an expert and certainly not with Ubuntu.

Cheers

As for UT, these features are important, but it's not an easy task. Palm was able to build a desktop server to handle their phone. And I'm trying to remember, but I think I needed to use their calendar to be synced....

Now you have some options, keep us posted about what you will discover. I'm sure many will be interested.

So it drives me crazy that it can't be done with smart phones (Android, LineageOS, or Ubuntu Touch) and a desktop. Instead, a third party, like Google, seems to be required. I'd rather not be forced to share all my daytimer info with the likes of Google.

Since syncing directly between a Palm Pilot and a desktop was possible, I don't understand why it's not possible with a smart phone and a desktop.

I wonder: Has anybody ever tried a direct sync using syncevolution on both sides? https://syncevolution.org/wiki/synchronizing-evolution-http-howto and/or https://syncevolution.org/wiki/http-server-howto

If you want mobile sync, than you will have to open a port from internet to your desktop acting as a server.

But NextCloud is the solution I know, maybe your calendar app on your desktop can sync ICS files or allow synchronizing with other softwares...

The calendar app in UT is compatible with CalDav protocol, so if your desktop app can work as a CalDav server than you don't need anything else.

Good luck

thank your very much for your answer. I thought about to synchronize via WiFi or even a usb-cable when I'm at my PC. This would be fine for me .... Are they any apps or solution which make this possible?
Thank you.

Synchronizing calendar might occur using a "cloud" system.
According to me synchronizing means that any operation on one side is replicated on the other side ; so it must use some kind of service put in the middle of the two systems.

With UT I use NextCloud, you can use any NextCloud service available or create your own self-hosted solution.

I hope this will help you find what you want.