I've heard some people with issues on it. And I think I might be one of them, I have yet to try mine on an LCD TV yet. But I think a good test is to hook up your PS2 via Component cables, and play a few PS1 games like that. If it handles the signals ok I think it will be ok. On my LCD for some reason when I play a PS1 game on the PS2 with the component cables, it has major video issues.
So if your PS2 is set up like that it might be a good test for you. Otherwise I am not sure how to tell if your TV can handle it or not. I have heard that most can, and I am still tempted to try mine to see what happens. I might just have some sort of issue with the PS2 and/or the PS1 game and not the TV.