I have got a similar problem. When some of my friends log in I can chat with the instant they log in, but some I can't even see log in. We tried creating new accounts but it's the same problem.
Is it something with the game or our connect?

same here, also the chat in lobby does not work

Having the very same issue; Can only see some friends, and if we can't see someone, them relogging does not help

i dont know how to even invite a new friend if i havent played in the same game with him/her?

had the same problem, but only on my laptop. my desktop was fine.

I turned off my windows firewall and it works like a charm again.

So what is the solution of that problem?

Hate when the staff doesn`t answer....

Please fix this riot.

Yeah, seems to be issues with inviting friends into games and the usual friendlist delay problem. I guess the best thing to do is to wait patiently, I am sure that Riot is working on the issue at the moment.

EDIT: Seems that there is a general delay for every action you do in pvp.net. If you create a game and invite people, it will take a few minutes until everyone even gets their invites. My friend just logged out and logged in, and now suddenly his status changed to "Creating normal game", even though he has not created a game. The last game he created and cancelled was 10 minutes ago.