The post was a little before my time here, but I'll give explaining it a shot sphere
The first problem for Lc is that there are a crap ton of places on 'nix where you *could*
put an icon for your app to use, including the folder of the app itself. There are several cases where apps from the repositories fail to properly get their icons right for a particular desktop/distro, where as with Win and OSX, there is only 1 place that is sanctioned.
The end result is that you have 3 choices with 'nix, you can -
. put the icon in the folder with your app and include instructions for how to use it, or
. you can do a LOT of reading for each distro, and setup your own automated way to do it, or
. you can put it in the most likely place and *hope* that it all works out
As to the *where* icons go, your most likely candidate for almost all systems is going to be in "/usr/share/icons/"
Even there you have choices, you can 'chose' to put it in the themes folder that the user is using, you can put it in the general icons folder (not all themes draw from there), or you can put it in all
the possible folders. Note- you will need admin privileges just
to place the icon somewhere outside of the users folder!
A secondary choice is in the home folder in a hidden folder for your program, where you would also place any preferences, individual to that user's scripts, etc (resources for your program in effect). This doesn't require admin privileges
Now, once you have figured out where your icon is going to go, you then have to create the directions 'nix will use to place it on the application starter for the menu or desktop launcher which vary by (you guessed it) distro and desktop. The most likely way your going to do this is with a desktop config file which goes (you guessed it) where ever the distro/desktop your user is using determines it goes. There are places more likely than not, and of course there is always the users directory in that hidden folder you made for preferences.
*The above is my most likely "guess" as to why Lc doesn't delve into it for the standalone maker, and they certainly are not alone in that as I mentioned earlier, however there are plenty of tutorials and tracts dedicated to actually configuring this yourself for your programs and Lc *has* been getting the icon right for Lc itself since about version 7.x or the late 6.x series (past 6.5). Before that, on more distros than not, I configure the launcher icons manually for Lc itself.
Hope that helps to some degree.
* My opinion only, not based on fact or knowledge, just an (un)educated guess
Edit 1 - Or where the Lc IDE is concerned, the original scripts that placed the icons may have just broken over time like the launch after install did, I believe 2.2.1 placed its icon correctly.
Edit 2 - the original Mc which started out on 'nix I had to manually configure the icon as well, so not limited to Lc.
Edit 3 -
It's been a while since I last had to deal with this, but if I remember correctly, setting the icon for my own apps before I had to copy some .png files to the /usr/ area somewhere and had to put an entry in a config file somewhere, or was issue a console command?
This has changed since Garrett wrote this answer, icons can be .png, .gif, .svg(specific format though), or any number of other graphic formats. Your still better off using the user's home directory and a hidden folder for the icon placement imho if you can swing it, as mentioned above, any folder in the filesystem is going to require admin privileges to write to it.
Packages added to the system through your package manager already have this permission granted, all pkg. managers require root permission to launch.