I have the same problem as you do. Long time authenticating and lag in client and game (cant play normal)
I got this on sunday for my ticket report. I have problems since 22.6.2017
Hello Summoner,
Eduard from Player Support here.
Thank you for the logs you have provided.
Wish I had better news but it looks like your connection to our servers is passing through a bad node that's outside of your ISP's network, there's nothing we can do from your side but we're going to use the info you've provided to investigate further and resolve the issue.
I can't provide an estimate for how long this will take but it's our top priority at this point in time. Please let us know if you have any other questions regarding anything else.
Have a good day!
Kind regards,
Eduard of Chaos
Player Support Specialist
Riot Games
"Why so serious?"