From the Protecting Your Account support page
You may not share your account with anyone, not even a friend or a family member. Doing so is against our Terms of Use, for a number of reasons that are listed below:
(read the support page)
Also taken from their Shared Accounts support page.
• You give your password to a friend or family member
Nooooo! Don't do it! The only person that should know your password is you. Don't forget that accounts are personal. Each summoner is unique, which means that when his account is shared, part of its personality is lost in the process. Don't give your password to that friend who wants to check out your skins or to that cousin who just joined the League and wants to know what a level 30 account feels like. You can always help them create their own account. That way, you can even start a team and play together.
Now from their Terms of Use (which you agreed to when you made an account)
1.4. Can I share or sell my account or login credentials? (No.)
When you create an account with us, we require you to select a unique username and password (collectively, your “Login Credentials”), which you’ll use each time you access the Game. You can’t share your account or Login Credentials with anyone. You can’t sell, transfer or allow any other person to access your account or Login Credentials, or offer to do so. You’re entirely responsible for maintaining the confidentiality of your Login Credentials. Please notify us immediately if you become aware of any breach of security, including any loss, theft or unauthorized disclosure of your Login Credentials.
Your account is ENTIRELY your responsibility, it is your fault for letting your friend on who then went on to be toxic and get you banned.