HDTV doesn't cause lag if you set configure your Wii to output at 480p.
Your TV on the other hand may cause lag but that has nothing to do with it being HDTV. The blame is on your TV manufacturer putting in flash preprocessing algorithms to slow you down.
Basically, if you play on an HDTV set, set your Wii to 480p (you need component cables). This will eliminate the need to deinterlace the video, which is what most lag is from. Playing with S-Video, Composite or Component set at 480i will make your TV have to deinterlace the video and can ruin gameplay.
Playing 480p on a 720p/768p/1080p HDTV has minimal scaling lag (less than 1ms. You won't notice). As I said, if your TV has flashy preprocessing disable this. Many HDTVs have this, but not all. Also, many SDTVs have flashy preprocessing so just because you don't have HDTV, doesn't mean your TV might lag.
Finally, there is a consideration of lag because of what type of TVs you use. CRTs lag least, followed by LCD/Plasma and DLPs are the worst lag. It doesn't matter if the TV is HDTV or not, the type of screen it WILL create a some sort of lag. (ie, a DLP SDTV will usually, but not always, lag more than a CRT HDTV @ 480p)
But please use the search feature. There have been 2 large multi-paged threads on this topic in the last month and I'm just paraphrasing the other threads. Will a moderator please lock this?