I've just packaged up a portable version of LoL for Linux, with a patched Wine embedded, that you can download and play without going through all this hassle. You just download the package, make it executable, run it, and you're playing (after downloading all the RADs etc. If you have an older LoL install and don't want to download everything again, the WINEPREFIX I'm using is ~/.lol, so you can move your old RADS to ~/.lol/drive_c/Program\ Files/League\ of\ Legends/RADS/ to avoid the download.
It should work on any distro, but so far I've only tested it on ArchLinux, so please let me know if it doesn't work for you, I'm pretty new to LoL but I think together we can create a badass portable package.
You can download the package here, and there are some other games, and some information about how this works in here.