That should probably be its own discussion. As I don’t get the feeling that @sam’s topic was about custom icons per category, but rather, that he doesn’t care for the default lock on categories that are restricted. Two different problems here as yours would expand to categories that do not have restrictions.
I simply wanted to point out that @sam’s issue is easy to overcome.
@jvzr How did you go about hiding the icon? I’d like to do the same thing on our forum, same principle that folks don’t need to be reminded if they have access to additional categories.
.badge-category i.fa.fa-lock:before { content: ""; } /* remove the existing icon */
An eye or slashed eye would be a good fit. (Doesn’t matter if it has been used for unlisted topics - it says the same thing, this is hidden/restricted).
As discussed earlier in this topic, it is a simple CSS fix to change the icon to whatever Font Awesome icon you prefer. Or did you try that unsuccessfully?
https://meta.discourse.org/t/alternatives-to-lock-icon-for-categories/24815/51?u=mittineague
except if you want the slashed eye use “f070”
http://fortawesome.github.io/Font-Awesome/icon/eye-slash/
Sorry, I did not read the whole thread or even look at the CSS 
(still think it needs to be fixed in the core product mind).
Changing an icon globally is very simple using APIs
https://meta.discourse.org/t/change-icons-globally-using-the-apis/87751