OK - hold on - let me get this straight - you're talking about a HDTV you bought in 2006 - and you have the gall to complain to me about lag? Are you serious? You do know that anything above 2ms response time is a piece of crap right and that no 2006 HDTV has any hope in hell of even matching that, right? It would be like expecting the NES to be able to render N64 graphics -it's that incredulous.
Anyway, in case you didn't mean that - let me talk about 'native resolutions' since it might be the crux of the problem -
Every HDTV has a 'native' display resolution - for some it's 720p, for others it's 1080p.
When you have something like the Wii that drops you back into 480p mode (if at that), it could well be the case that your TV does not natively support this display resolution and therefore a lot of postprocessing has to be applied to convert this on the fly by the TV's CPU - hence leading to lag.
Go ahead and read this entire article - there are some 'solutions' there you can try - but there is no such thing as a magic bullet - because it's the deficiency of your hardware.
http://www.lg.com/ph/support/product-help/doc-2122921-en-LGEPH
It also explains something about this native resolution issue that I am talking about -
Again - really - this is not my problem - it's yours - you bought the TV, not me. Take it up with them. Any gamer that doesn't have a HDTV with at least 2 ms response time or less has no right to complain about input lag - you get what you pay for. And if you still want to complain - make sure that certain person isn't me, because I have nothing to do with your purchasing decisions.
And also, quoting 'Bittrip Runner' (whatever - you say it's a 'rhythm game' - I say it's not the same kind of fast-paced rhythm game as Parappa - and seriously, that article I linked you to was written by the original dev) runs smoothly or 3rd Strike demo - it's MEANINGLESS - don't you get this by now? These games were 'altered' in ways so that it will more or less run acceptably on every shitty HDTV out there - we can't exactly do that with an emulator now can we? It's not like I have the source code to each game and I can tweak a few knobs and have them run at a different refresh rate or do some tricks.
Sorry, but I'm not going to be a counsellor for people who buy HDTVs and expect zero-lag nirvanas. Read that article, and accept the fact that this is not my problem - it's as simple as that. You're being incredibly harrassing over something that is not even my fault - take it up with your TV manufacturer if you're so passionate about it - they sold you the thing and promised you nirvana, not me. Or you should have just held onto your old CRT TV instead of throwing it away.