Please launch Activity Monitor and check for the process for Dynamic Link Manager, if there is any select and end it.
Once done, then try to open Lightroom and see if the application launches or not.
this was my first idea as well and I already checked it, but the Dynamic Link Manager is not listed in the Activity Monitor. So I'm unable to close it there.
Did you try to restart the computer, also please reinstall the Application once by removing the Preferences when uninstalling the Application.
Yes, I did restart the computer, but I will try to reinstall the application. I already faced problems with Yosemite in combination with the new Lightroom/Photoshop applications and downgraded everything to version 5 of the Adobe applications. I was hoping, El Capitain would work in conjunction with the most recent LT/PS applications, but in case the problems will persist, I will once again downgrade to the old versions. It's a pity, that I'm not able to use the new features with this set-up, but better than being not able to work with LR/PS at all.