Burn? No. Unlike a CRT, there's no energetic electron beam striking anything. There's no destructive momentum transfer in an LCD, only a gentle change in optical polarization.

What *can* happen, however, is for the liquid crystals to become a bit sticky. If forced to remain in a particular position for an extended period of time, they'll tend to favor it. This stickiness is not great, however, and it is easily overcome. Just leaving the display off for a day or two usually suffices. In the rare stubborn case, displaying an all-white and then perhaps an all-black screen (not by manipulating the backlight state) for a day or so will fix it.