LCD's dont burn as such, but they can gain a memory. So if you display black for 10 hours, they 'can' remember that, and you may be able to see darkness in the areas which were black.
However unlike CRT, and Plasma technology, if you display the inverse for an equal length of time (so 10 hours of white bars), the memory effect is erased.
For a computer display which is fixed in a certain way for hours (Say the flight boards at an airport, LCD memory is just as real as Plasma/CRT). On the other hand, as the video signal you feed an LCD TV is much more random/dynamic the chances are it will be constanty erasing the 'memory' effect as you watch different programs.
So in general its 'safe' to consider LCD as impossible to burn, but yes in some situations a similar effect is possible.
(Just think how long it would take to erase a 'memory/burn' on a LCD that had displayed a fixed image for 1000 hours!)