This is a really old thread, good god.

I use XSplit to stream my games, or Bandicam if I'm just recording something like osu! or KanColle. Then again, I usually put my games in windowed mode if they aren't already in windowed mode, so I'm not sure how it'll work on a fullscreen game like LoL. Try fiddling with the settings and if that doesn't work, get a new CPU if you can afford it or try something else if all else fails.

Edit: Actually, I've learned that sometimes the game lags because it's trying to capture all the frames, so try looking back at the recording before poking at anything else.