Thank you for your comments.
Well, first, I think I have shown that there is something wrong or unpolished with the distro, right (I did run it as the user)? This exact procedure did work with other distros and I see no reason why this shouldn’t work given that I simply install a supported protocol and package.
The reason why I want to use RDP is irrelevant to the problem we are discussing here. By using something else instead you haven’t fixed the underlying issue of the tool that is actually supported. However, I am happy to explain: RDP is simply an always working, no nonsense, no additional installation needed protocol and tool, that makes it very easy to connect from my Windows machine. Further, I can also connect from my company laptop, where I can’t install further software. In regards to security, I am aware of it and my network is shielded from the outside with a dedicated hardware (IPFire) firewall and the protocol is only inside my network allowed.
As I was using Lubuntu out of the box + XRDP and have shown that it doesn’t behave quite as it should (it’s reproducible as well), I was hoping somebody would pick it up to fix.