The trick is - do you mean actually turning off the LCD, or merely the LED illuminating it?
LEDs are expected to have a lifetime of in excess of 30,000 hours (which is of course, 3½ years) in continuous use, probably more like 100,000 hours, and of course, it would almost certainly depend on how hard they are driven. I do wonder how they actually figure this.
The LCDs themselves have been used in alarm systems, continuously operating for five years and more. I think you could expect at least this lifetime.
Earlier production LCDs in calculators and communications radios have tended to degrade - even without regular, intermittent use - over the years, going black. I really do not know whether the materials presently used are more stable, but LCD computer monitors seem to be pretty durable. It is very important that the drivers deliver symmetric drive waveforms and the display receives no DC component
Older small LCD panels used EL - electroluminescent - illumination with a high voltage, high frequency inverter. These were less efficient and in fact the phosphors did wear out over only a few hundred hours, so for this reason alone the illumination was generally arranged to shut off after a short period of inactivity. I do wonder how durable the phosphors used to implement [u]white[/u] LEDs will prove compared to those used in the EL and fluorescent lamps which we know wear out within a few thousand hours though again, CFLs advertise longer life. Phosphor degradation in fluorescent lamps will be due to the intense deep UV component of the mercury arc and ion bombardment; white LEDs have no such component.
Did this answer your question in the end?