I got an answer from Pro support:

"Hi Udo,

The LimeWire application has no control over whether your computer can connect to the Gnutella network. Also, OS X has a built-in firewall, which may need to be configured to accept Gnutella traffic. Please try the following:
-Uninstall all versions of LimeWire, using the Uninstaller in LimeWire's folder.
-Delete all LimeWire aliases and installers from your desktop and Dock, and remove all instances of the installer from the download manager of your Internet browser.
-Reboot your computer.
-Go back to the LimeWire Pro download page, and download the installer to your desktop.
-Reinstall LimeWire Pro.

Thanks,
Zenzele"
I will try it!