I'm currently running LoL with my Asus G50VT Laptop. I have been able to successfully run the game on the highest video settings at full speed (typically around 120fps out of combat, and 85 in) without graphical problems. After the latest patch (8/11/09 I believe) the ENTIRE ground floor of the game would go black as soon as I moved the camera; I also could not see spell effects. All the buildings and units were fine, but no trees, grass, or snow.
Strangely, turning down the Character Detail in the options to LOW (medium did not work) made the game worked properly. It's strange because the characters do not have issues, it's the ground that does, but the character detail fixes the problem.
I should also mention that my laptop is said to come with a 9800M GS, but Asus insists that I get 9800M GT drivers. Using the GS drivers I get serious issues and the NVidia control panel no longer works (all video control for full screen games, resolution, color, the works).