As the follow up of these issues:
I think I narrowed down one of the possible causes. The problem seems to be caused by the new summoner tooltips, which is appeared when you hover over summoner's name in friend list, chat group, or custom game.
There is an apparent memory leak caused by it. As you hover more and more people in the list, the memory usage will increase. At some point, memory usage can become so high and potentially crash the client. The only way to fix this is by restarting the client.
This is probably because of the object handling each tooltip is not deleted correctly. Or maybe garbage collector goes wrong.
To PBE users, for now the solution is by not hovering the summoner name in friend list, chat group, or custom game.