Narpas: Nothing I said was wrong. I said my explanation was simplified and there's many other elements to it that I intentionally left out so as not to bombard her. Also, I never said response time = input lag.
Console > Cable > Display
or
Console Graphics Card > Output Chip > Console Output Connectors > Cables > Display Input Connector > Input Chip > Screen
Sammy: All TV's "lag", even CRT's. Hooking up Smash4 on a bad HD TV will still be laggy if the response time is high, even though it natively supports HDMI. The questions is, how much do they lag? Good ones will have a response time so low that it is not discernible and therefore does not affect game play enough to matter.
If you have the resources to invest in a good LCD, I think it's worth it. Someone people would rather lug around old heavy CRT's because it makes them feel good, which I completely understand. In the end, if you just play with your friends and aren't worried about becoming competitive, then keep on enjoying playing on your setup. If you want to get competitive though, you will want to look into getting an optimal setup.