Might be best to read up on bin files etc. but here is my way of doing it (note I am in no way a linux guru)

you normally have to make a bin file an excecutable first.

so use

chmod +x thenameofthebin.bin

then use ./thenameofthebin.bin to run the file (you may have to su)

look where you downloaded LimeWire, further down in small writing it gives a link to download Java (its a big download btw)

Then look at the thread on here labeld No Java VM for help with installing Java properly.

Hope that helps.