NOTE: Before you do this method you must know that this method is done by using riot support and has a success rate of 40% and you need to know a lot about the account and the user before you try this method. This method is a lot easier of you're trying to steal the account of your friend who doesn't play LoL anymore or isn't active.
Choose the "recovering account" tab when you're on the riot support site.
Don't post here if you do not know the email linked to the account or... if you're just curious and want to know how to change it you could reply.
Btw if this didn't work, just keep trying and try it on another account. I've tried this on 8 accounts and it only worked on the fifth one, if you want proof I've recently made a thread in the achievements sub-forum if you want to check it out.
Don't forget to post a screenshot if this worked ^^
EDIT: Sorry for the weird colors and stuff, my spacebar is broken and im just using cntrl+v with a open space.
Edited by Aki, 05 May 2016 - 05:35 PM.