I know the initial reaction to this question is "no" and "it can't be done" and "you shouldn't need it, you are doing something wrong". What I'm trying to do is get the users LAN IP address, and display it on the web page. Why? Because that's what the page I'm working on is all about, showing as much information as possible about you, the visitor: https://www.whatsmyip.org/more-info-about-you/
So I'm not actually DOING anything with the IP, other than showing it to the user for informational purposes. I used to do this by using a small Java applet. It worked pretty well. But these days, browser make you hit agree and trust so many times, to run even the most minor java applet, that I'd rather not run one at all.
So for a while I just got rid of this feature, but I'd like it back if possible. It was something that I, as a computer consultant, would actually use from time to time. It's faster to go to this website to see what IP range a network is running on, than it is to go into System Preferences, Networking, and then whatever interface is active.
So I'm wondering, hoping, if there's some way to do it in javascript alone? Maybe some new object you can access, similar to the way javascript can ask the browser where is geographic location on earth is. Maybe theres something similar for client networking information? If not, perhaps theres some other way entirely to do it? The only ways I can think of are a java applet, or a flash object. I'd rather not do either of those.
As it turns out, the recent WebRTC extension of HTML5 allows javascript to query the local client IP address. A proof of concept is available here: http://net.ipcalf.com
This feature is apparently by design, and is not a bug. However, given its controversial nature, I would be cautious about relying on this behaviour. Nevertheless, I think it perfectly and appropriately addresses your intended purpose (revealing to the user what their browser is leaking).