Does LCD TV screen damage your eyes?

Well too much of anything can be harmful.

If you turned the brightness of the LCD as high as it went and stared at a white flashing screen for some time I'm pretty sure that couldn't be "good" for you.

But for general use I know of no one having eye problems from using an LCD monitor.

Actually LCDs are safer on the eyes than traditional CRTs as the refresh rate (Hz) rating doesn't have to be high and the screen updates in a way that causes less strain on your eyes.

I use an LCD for hours on end day after day. On my last eye exam I was told that my vision and health of my eyes had improved since I switched from using a CRT.