All HDTVs have lag when dealing with a low-resolution or interlaced signal. The cheaper they were when you bought them, the more likely they are to have really bad lag.
The main issue is that the signal is interlaced, and only CRT TVs are natively capable of deinterlacing, while everything else has to run the video through a filter; that takes time, potentially a lot if the manufacturers didn't write a quick filter, or if they added bells and whistles to make the picture look nicer (post-processing is great for movies, not so much for competitive video games).
The main issue is that the signal is interlaced, and only CRT TVs are natively capable of deinterlacing, while everything else has to run the video through a filter; that takes time, potentially a lot if the manufacturers didn't write a quick filter, or if they added bells and whistles to make the picture look nicer (post-processing is great for movies, not so much for competitive video games).