I know nothing of LoL, but, per that speccy, that ram seems to be running a very low speed. Is that its rated speed? Athlon can go up to 2133 mhz, yours is at 798 mhz. Is an XMP in your bios for that Ram?
I would also check against a different game that is not online dependent, but for all I know part of LoL is not online. Best to remove as many possible factors as possible.
Your cpu should be good enough for a 2009 game. Per the LoL recommends, it looks like you should be ok.
Definitely close Chrome, it uses a decent amount of cpu and ram.
Also keep in mind if you are playing on a 60hz monitor and your frame rate is over 60, it can get choppy. Does LoL have vsync in its graphic options?
I would also make sure I was within the least acceptable resolution in Windows for that card and that game.