Ok, so I haven't managed to record this or anything but this has happened twice now in the last two days while running the beta client. The first time, I'm in the middle of the bot lane and the game just freezes out. I can alt tab and CTRL ALT DEL but it won't actually change window, so effectively I'm locked out of my PC and have to force reboot it.
The second time the exact same issue happened trying to load into a game from draft pick. As I went in, the cursor loading circle kept spinning, as did the bottom but non of the champion portraits filled in, then when I tried to tab out, same thing again. Locked out of the laptop by the client. So I managed to log out by CTRL ALT DEL and reload the client only for it to multiple times, fail to load the game and freeze out the same way.
It brought up some error message which said there was a potential DirectX issue which is stopping LoL from running properly, however this happens on no other games that I play through steam so I'm doubting it is DirectX?...
The way to remedy this issue was to, on both accounts, reload the game using the legacy client.