I don't know if this is the exact issue I was having, but it's similar enough I'll comment.
For months, champion select would just randomly crash my whole computer. It would either just black screen or blue screen and shut down, or it would freeze and the graphics would become pixelated and my whole computer would make this awful whirring sound and I would have to hard reboot. If I hadn't selected a champion, the lobby would continue for my husband next to me like I was still there and disband when I didn't pick a champ. If I had picked a champ, it never realized I left and I could log in after summoning had started (if I logged in before summoning, it kicked everyone out of the lobby, so I had to pray i had the right runes and masteries up).
I spent 2 months with Riot support updating graphics drivers, uninstalling and reinstalling with custom installers, turning off firewall, etc and nothing fixed it. I have virtually the same computer as my husband and he never has this problem. And one day someone told me they knew how to fix it and I was like "At this point I'll try anything" because I couldn't play ranked it was so bad. And it made sense to me because I use a logitech mouse and keyboard. My husband does not.
The steps were:
-Go to: C:\Riot Games\League of Legends\RADS\solutions\lol_game_client_sln\releases\x.x.x.xxx (folder with LARGEST number IE 0.0.0.238)\deploy
-In this folder, RENAME two files, LogitechGKey.dll and LogitechLed.dll. This should hopefully cause your client to not crash anymore.
(source: https://www.reddit.com/r/leagueoflegends/comments/1gn3vt/fix_crash_after_champion_select/)
This fix took me about 20 seconds to do and I have not had a crash since. So if you use any logitech software at all? I'd recommend it's at least worth a try! And I hope it helps you.