A picture can not really burn in on an LCD monitor but it is still advisable to use a screen saver (or another picture) - every twelve hours just for some seconds, as explained by the monitor manufacturer "Samsung" on inquiry.
"Do flat panel displays still need a screen saver?"
In LCD monitors there is no cathode ray that could burn an after-image like in conventional TVs or monitors. Just as there is no hot glass like in plasma screens, either. And yet, LCD monitors have a "memory effect", too. Because during a still picture, the liquid crystal molecules are aligned in a certain way and can become sluggish if there are not moved. The effect is irreversible like a "burn-in" but can be prevented by the employment of a screen saver that becomes active for some seconds every twelve hours.
Should there really be a picture that has become permanent on the LCD monitor, it is usually enough to display an entirely white screen. The duration of displaying this white should be at least for as long as the previous picture took to create this "memory effect".