I'd poke around the Runescape forums or "google" to see if anyone has done this. What we know is that the code folk write in JAVA could have dependencies on the platform. That is, it may not run everywhere. Today I find most folk unwilling to accomodate other OSes or users that don't have any interest in programming, that is, dive in and fix the errors.
In short, find a linux runescape discussion with google.
Alright, so I installed Linux Mint 13 about 2-3 months ago and have been hoping to play Runescape on my computer, the specs on my computer would be able to easily handle this game w/ Windows 7. However, with Linux I'm not even able to log in to the platform. Java just doesn't seem to be giving me a good time. Is there any way to fix this or get around it?