Ok so apart from ticketing which takes too long and too much effort there is this method, it's a major flaw in the league of legends source code......
Step 1 : Go to the league of legends website and click on ' support '
Step 2 : After logging into the support page on the desired account. left click then select ' view page source '
Step 3 : Click on the url https://support.riotgames.com/hc/fr"
Step 4 : Left click / view page source again, this time press Ctrl + F then type email.
Ok now that we have the email, your best attempt is to try log into their email with their league username or password.
It doesn't work all the time, but it's simple / easy to do, and you could potentially make more money this way.