New Rift lags horribly during teamfights

There was a promise at some point (I don't recall where) that the new Summoner's Rift would actually improve performance. My computer's never been fantastic, but I could always play the game without issues on lowest settings. Now, I can't even participate in teamfights without lagging behind a second and a half and dropping to 2 FPS. All my settings are still on lowest, nothing's changed, and I can, for instance, play on Twisted Treeline just fine.