Login Problem: When two people login from same place it doesn't work

So here is the problem that has been continued for past few months.

Two of my friends live in same place, and when they try to login to League, they both are unable to login. Instead what they have to do is one of them login first after a long wait (around 30min) and start a game when another person start logging in. Once the other person logins too, the other person come out and join him. Most of the cases, the person who logged in first always get an error and get disconnected from the server, so it takes few attempts until we all can play.

I have no idea what is the problem, and I am not tech savy. They both are using Mac. What could be the possible problem?