Contact support about it. You cannot fully delete the account, but deactivation is an option.
We can disable your account if you wish. However, there is no disadvantage to keeping an account active, even if you don't plan on using it, and once we disable an account, we won't be able to activate it again. Your username, summoner name, and registered e-mail will also remain in use in our system and cannot be used for a new account.
If you wish to disable your account, please contact firstname.lastname@example.org. Please mention "Account Deactivation" in the subject line and include your username, summoner name, server and email used when registering the account in your ticket. Also be sure your account is currently linked to the e-mail you are contacting us with.