Sounds like there might be a problem installing LW on OS 10.15 Does anyone know if others have successfully used the new version on 10.1.5 since the java upgrade?

There are two things you can try until the developers track this down. The first and easiest is to download the OSX version that is built directly from the CVS sources by Jens-Uwe Mager
Here's the link
http://baghira.han.de/~jum/LimeWire.html

If that gives the same trouble, try doing a clean install: Run the uninstaller, search your hard drive using Sherlock for any files called "limew" to find any old preferences that the uninstaller doesn't touch, restart your machine and download a fresh version.

Do post back to help others if you find something that works.