Well, the problem is on your end and it isn't on your end - at the same time.
I've done some digging since the critical error bug first appeared. And the one common factor I have found is the time that the bug appeared - and it seems to go back to patch 9.13 for some people. What I think is that the hanging problem coincided with the push by Microsoft to implement the 19.03 or May Update Patch to Windows. This particular patch has not been playing nice with some hardware and software, which from what I have found so far has included League.
The update of Windows, combined with two pushed updates by Riot, have led to some instability issues. For example, if you install League on a separate hard drive, then it can trigger the client crash (even though it played nice with League before). If you have some hardware that uses certain USB devices (including mice), then League and/or Windows can trigger the client crash.
On one hand, it shows a lack of preparedness by the devs for the WIndows changes. On the other hand, it shows that perhaps some things could not have been anticipated or planned for.