Can you list down your full system specifications?

I suspect the lag is due to a weak graphic card. Crysis Warhead is quite a demanding game and still is today. What you could do is like what Firagaz mentioned, reduce or switch off the AA / AF settings entirely as these are known performance hitters. You could download a software called Fraps and it can help monitor what FPS you're getting.

If you see the bench below for HD 5750 (i couldn't find HD 6670, the HD 5750 is slightly faster though), it can only churn out 17.7 min FPS under 1680 x 1050 resolution, which is basically unplayable.

http://www.anandtech.com/bench/Product/537

Actually, FPS is quite a subjective experience. But from my personal experience with games (after so many years), i find that "smooth" gameplay occurs only if you can hit roughly above 40 FPS. In fact, Guru3D also summarized very clearly here. I've tried gaming with a HD 6670 at full 1080p resolution on Rage, and it churns out around 25 - 30 FPS, which to me is still playable but i find it laggy at times. Definitely not the "smooth" that i'm looking for.