You can attempt to speed up LimeWire by enabling the JIT yourself. This can be done by opening up the file "LimeWire.lax" in any text editor. (LimeWire.lax can be found in the same folder that the LimeWire program is in.) Look for the line that reads:
lax.nl.macos.java.compiler=off
and insert a '#' before it, so it reads:
#lax.nl.macos.java.compiler=off

Then save the file and start up LimeWire.

I cannot guarantee that LimeWire will continue to work. But if it does, it will be a little faster.