I really dont know what solved the issue but both the locate libvtksys & locate libvtk return locations now! Maybe it was the sudo updatedb?
Also the tools of library X started to work. I will restart the system to see if this state is now persistent.
[Edit]
My apps and the tools of library x still work fine after a reboot. I hope that this issue is persistently solved in my case.
Thank you so so much for your quick help @ferdymercury! You really saved me.
Any idea what could have been the problem? So other users with this kind of problem find a quick solution?