I'm no expert but your console log states that you have 1,96GBs of RAM, if so that's probably the problem because I have about 4 GBs and it's all in use when I play HoN, when I'm running too many extra programs it causes my game to freeze etc.
Other than that, I'm using Windows instead of Linux so something in your OS might cause problems as well.
I guess it's not a storage problem, since i had such problems in the past with 2GB too and the issues were completely different (in the beginning slight lagg and then hon hangs up, finally it ends itself).
But maybe they are different if u haven't enabled ur swap?