You need to know the concept of the PATH environment variable. When you give an unqualified command name, the system searches through all the directories in the PATH looking for an executable of this name, and launches the first one it finds. So adding the limewire directory to the path will let it find runlime.sh:
However, there are several problems with this; firstly, the program's called runlime.sh and not limewire as you requested. Secondly, the script may well assume that the current directory is /home/user/limewire, and might not work from any others (I know that Eclipse and Azureus at least do this and wouldn't be surprised if it was true for other apps). Also, from a tidiness point of view it's nicer not to add a new directory to the path for every new app that starts like this.
What I would do, then, is create a small shell script to act as a wrapper. Something like:
# Launch Limewire
and save that file as 'limewire', make it executable and put *that* somewhere in the path. On most distributions, it's customary to put small personal executables in the folder ~/bin, and a lot of them will automatically add this directory to the path if there's something in it (Debian at least does). In any case, put this script somewhere in the path (move it to /usr/local/bin as root if you must) and then you will be able to launch limewire by just typing limewire.