I see everyone got this same error, simple fix that worked for me and others.
Go to control panel > Network and sharing center > Change adapted Settings > Properties. Now when ur at the properties of ur internet connection go to "INTERNET VERSION 4(TCP/IPv4)" will say, double click on IPv4 and at the bottom select preferred DNS to 8 . 8 . 8 . 8. And Alternative to 8 . 8 . 4 . 4. And thats it click accept, and open LoL client.