I can't add a specific friend in league of legends

Solution 1:

It seems to be a program problem, try to contact Riot technical support adding a screenshot with the returned message.

Solution 2:

You or him need to remove some of the friend requests you all sent out...

You can only send a certain amount of request... so you won't be able to add anyone unless some of your request are accepted or removed.

Solution 3:

This seems to be an ongoing problem, and there has been a notice sitting in the game client for quite a while:

Even though you posted this before they acknowledged the issue, if you (or someone else) are still experiencing the issue, you can try Riot's suggestions. The link in the screenshot just leads you to a Twitter post of those suggestions:

https://twitter.com/RiotSupport/status/1218333629606055936