That is the Standalone version or Offline installer version. It just means you install from your computer & not over the internet. It tends to be a lot safer, especially for Java.

You could see if this version works: LimeWire cvs builds (4.13.4jum489) but note, that CVS version has not been updated in over a month.

Although I think with later osx 10.4 updates it makes java 1.5 the default for all programs, perhaps see this just in case: Setting up Java 1.5