This same thing happens to me all the time.... It also happens occasionally after I lock in my champion and other people start to choose/lock in their champions. Whichever person was picking prior to the client freezing just will have their timer stuck at 0 and it won't show anybody else picking, then after waiting for whatever amount of time I need to for champion select to end it will say in the chat:
myclientdoesntsuck1 Has left the room
myclientdoesntsuck2 Has left the room
myclientdoesntsuck3 Has left the room
myclientdoesntsuck4 Has left the room
But I am still in the room, stuck in champion select. And I will stay there unless if I restart the client, re-log in, and then it will leave me at the 'You have disconnected, click here to reconnect' page, with that orange button in the center to reconnect to the game.
Please Riot, this bug has lost me promos... FIX THIS PLEASE!
EDIT: So 1 month later a similar issue happened, I joined the lobby of a game and was able to pick my preferred champion. Then when bans were almost done the last summoner's ban timer got stuck at zero and it didn't show who they banned and the client stayed that way until I was kicked from the lobby due to not being able to lock in my champion.
Riot needs to get off their butts and actually get to work on FIXING their game. Rather than constantly rolling out these huge meta-changing patches into a broken glitched and buggy game. Riot, do yourselves a favor, and listen to the community.