From here, if you’re still having issues, you’ll want to make sure that your computer’s clock is synced up. If it’s out of sync, it may be preventing you from connecting to the League of Legends servers.
If none of these above solutions work and you’ve double-checked that the League of Legends servers are up and running, then Riot has a couple more solutions you can try on its website, such as configuring your DNS and disabling killer network advanced streaming.
Source: https://www.distractify.com/p/unable-to-connect-to-login-queue-league-of-legends