The lag on a modern HDTV of decent quality is NOT going to be even slightly noticable. My Panasonic plasma has a response time of 0.001 milliseconds.
The LCD component itself might have a lag that small, but its impossible for an SD signal to have that little lag displayed on an HDTV. The least lag of any line doubler is an XRGB series box, and even they have a lag of one field (ie: half a frame) which is 16ms. Most (probably all) scalers built into TVs are going to lag by at least an entire frame (which is 33ms) since they need to wait for an entire frame to be displayed before they can scale it and then send to the LCD, which will also take some time.
That .001ms time Panasonic quoted is probably the time it takes for the actual pixel to change color once the voltage reaches it. This is great for reducing motion blur and ghosting. There is a lot more to an HDTV signal path that that though.
Now, the older shittier Walmart HDTVs lagged horribly, like 250ms or more, but the new ones have almost none, even the Vizios. They are probably 50ms or less, which is absolutely fine unless you are a Virtual Fighter 3 god or something.