from:
https://www.playonlinux.com/en/topic-14718-cannot_even_get_to_install_in_league_of_legends.html
Step one:
Open terminal and enter the next command on the terminal
sudo -i gedit /etc/hosts
Then enter what {ego} said
24.143.193.16 l3cdn.riotgames.com
64.202.189.170 pvp.net
50.57.198.72 support.leagueoflegends.com
66.151.54.140 beta.lol.riotgames.com
216.133.234.23 lq.na1.lol.riotgames.com
216.133.234.22 prod.na1.lol.riotgames.com
216.133.234.21 chat.na1.lol.riotgames.com
216.52.241.153 ll.leagueoflegends.com
23.21.255.17 http://www.leagueoflegends.com
23.21.255.17 leagueoflegends.com
216.133.234.24 store.na1.lol.riotgames.com
216.137.47.27 landing.leagueoflegends.com
72.21.91.29 crl3.digicert.com
205.234.175.175 crl4.digicert.com
199.21.207.10 ocsp.digicert.com
It has worked for me... thanks man!! I really apreciate it...
Also I followed this guides :
https://boards.na.leagueoflegends.com/en/c/help-support/9wQEUhcm-linux-playonlinux-file-removed-to-install-league
https://www.playonlinux.com/en/app-3102-New_League_of_Legends_Client.html
And made some extra modifications to the host file to avoid some malware and obnoxious ads on my chromiun and chrome browsers