Aha! This issue does look like it's caused by a makeself problem! According to the site (http://www.megastep.org/makeself/), :

"Important note for recent GNU/Linux distributions: Archives created with Makeself prior to v2.1.2 were using an old syntax for the head and tail Unix commands that is being progressively obsoleted in their GNU forms. Therefore you may have problems uncompressing some of these archives. A workaround for this is to set the environment variable $_POSIX2_VERSION to enable the old syntax, i.e. :
export _POSIX2_VERSION=199209"

I'd be interested in hearing from a user who has had this issue. Any one having this problem and willing, please try this and reply with results:

Open a terminal window (xterm, konsole, etc) and cd to the directory where you downloaded the installer. If it's on your desktop then just do a 'cd ~/Desktop'. Once you are in the same directory as the installer, run this:

export _POSIX2_VERSION=199209 && sh LimeWireLinux.bin