Do graphical/pixel mapped LCDs need a screensaver?
The quick answer is, yes.  But not in the same way as the old CRT's or Plasma screens.

The primary thing that degrades in any LCD is the backlight.  Over the lifespan of the LCD, the backlight will get progressively dimmer.  This is true of all backlights:  LED, Cold Cathode Fluorescent, and Electro-luminescent.  To slow down or prevent this degradation you can dim or turn off the backlight when not in use.  

The next thing that degrades in LCD's is the LCD "material" itself.  This happens to the Blue sub-pixels more quickly than the Red or Green, and happens because the light-energy shining through the LCD gets absorbed by the LCD itself and heats it up.  For most "direct view" LCD's this is a non-issue.  There just isn't enough light going through the LCD to do anything.  But if you have a video projector that is shining a very intense light through the LCD then you need to consider this.  Also, if your LCD is in direct sunlight for a lot of the time then you might have issues.  The solution to this is to turn off or dim the backlight/projector-bulb.

What I cannot tell you is how important it is to do the backlight dimming.  Some cheaper displays will have more problems than better quality displays.  Without knowing specifics, I can't tell you specifics.  I can tell you that I design equipment that is supposed to run for 10+ years (24 hours a day, 7 days a week), and we always dim or turn off the displays when not in use.