How to fix League’s ‘cannot connect to authentication service’ error code
If you are getting “cannot connect to authentication service” error while playing League of LegendsYou may have any problems.
It could stem from a faulty internet connection, interrupted firewall, or something else entirely. Error messages can occur during champion selection, at the login screen, or in the middle of a match. Either way, this problem is easy to fix.
The first thing you should do is check the status of your server. Chances are the problem is not on your end and Riot is the one to blame. If that’s the case, all you can do is wait. To check your server status click here.

Once you’ve checked your server status and everything is in order, log back in League and upload a game. If the error message pops up again, your next action is to troubleshoot and update your firewall. Sometimes, for whatever reason, the firewall blocks access to your internet connection, resulting in this problem.
Under normal circumstances, firewalls are not designed to block your communication with League, but if they are out of date, they may misbehave. To work around this issue, you can either disable your firewall completely or update it.
If you’re using the default Windows firewall, you can turn it off by clicking Start, Control Panel, and System Security. Once you’re there, navigate to Windows Firewall and click Disable.

If that doesn’t work, there is a last resort. Temporarily changing your DNS settings is a quick fix to the problem.
To change your DNS settings, open Control Panel, click Network and Internet, Network and Sharing Center, and Change Adapter Settings. There, right-click on your network (Ethernet or Wi-Fi) and select Properties.

Select and check Internet Protocol Version 4 (TCP/IPv4) option and again click on Properties. Finally, click on the option Use the following DNS server address and change it to Google Public DNS (8.8.8.8, 8.8.4.4).
https://dotesports.com/league-of-legends/news/how-to-fix-lol-unable-to-connect-to-authentication-server How to fix League’s ‘cannot connect to authentication service’ error code