I must say that certain Android devices has been reported to have had half of their screens going black without being dropped. In your can, however, it is certain that the behavior is entirely owing to its having being dropped. First I would suggest you perfom a hard rest and observe (do note that this will erase all user data and apps so perform a backup first. A hard reset could work particularly if the blank half rotates as well when "Auto-rotate" is active. The screen display connector (the one that connects to the phone's motherboard from the screen) may have partly disconnected upon the fall. In the extreme, the one half of the LCD/digitalizer may have suffered physically upon the fall and consequently went bad. An LCD replacement can be able to resolve the issue if the latter is the case. The YouTube video here demonstrate the perfomance of a screen replacement on you LG device model.