The game is running absolutely fine on my machine, and mine is also an 4870 ATI-machine... I'm even running it over the performance limit to - aside from a bit of lag updating the LOD especially when looking around absolutely no issues...
With all the various games and computers I had, only one game gave me constant issues and crashes: Fallout 3...
Onto the game: The attention to detail is incredible, Rockstar is in a league - no, world of their own! The controls are very thought out, I just can't define an axis? I couldn't bind my wheel to the car controls - quite an oversight imo...
It pains me a bit to say this, but GTA4 has a better driving surface than LfS, by quite some margin too...