I have gotten this error for months now, almost exclusively at the end of games. It has been a couple weeks now where I'm now getting the errors within the game as well. It will usually occur once to twice per game now. My client will just black screen until I alt tab and clear out the error message and am brought back to the league launcher. Any help is greatly appreciated!
A core dump is something a program makes when it crashes horrifically, and they can take up a bunch of space. If you failed to create a core dump (which sounds like what the error is implying) then you might be low on disk space. You could try searching your Riot Games folder for the old core dumps (I think they end in ".dump", but it might be different) and deleting it, or you could try and free up other space on your computer.
If you aren't low on space, maybe try reinstalling the game.
