DIAGNOSIS That's power supply coil whine. It's an annoying but generally harmless manufacturing variance where components on the internal power board vibrate at high frequency. It's more noticeable in quiet rooms and with some specific brightness/refresh rate combinations.
FIX You can try to 'mask' it by adjusting settings. Change the monitor brightness (sometimes 50% is worse, try 75% or 25%). If you're using a high refresh rate via overclock or specific modes, drop back to standard 60Hz. Ensuring the monitor is on a stable, non-vibrating surface can sometimes reduce resonant noise.
IF THAT DIDN'T WORK If it's severe and the monitor is under warranty, contact LG. Some units have it worse than others, and a replacement might be quieter. There's no user-serviceable fix short of replacing the power board, which might have the same issue.
HEADS UP The whine might change pitch or intensity when the screen displays very bright or very dark scenes. This is normal for this type of noise. It doesn't indicate an impending failure, just an auditory nuisance.