This is how you change your league of legends shortcut Icon.
Download that cool image you like
Find a website that will convert images to the .ico format
Convert your images to the .ico format and save it to a directory eg. a file on your dekstop or something
Now right click your shortcut and select properties
Then select change icon
Then click browse and go to the folder or directory where you saved the .ico file and select the .ico file
Now if you want to change the exe icon... that is a bit tougher, you can change it but I think it requires some software, I just know it is harder