I have four lcd's including a sony bravia 52" LED LCD (KDL-52EX700) and all works with 240p. So lcd's that doesn't work with 240p is in the minority. I get why people rather stick with crt's because that was what these retro systems where designed to be played on. I have two CRT's myself that I use those for testing purposes in my office. However for my gaming needs, I rather sit comfortably on my couch and retro game through my 52" sony bravia because 240p looks amazing on it.
Btw you can easily test to see if your hdtv lcd with 240p by connecting the composite video rca (yellow rca) to the "Y" input. If it display a black & white pictures, your set supports 240p.