When the screen blacks out try shining a torch at an angle close to the screen to see if there is still a display there. You may have to look very closely to see it.
If you can see the display then there is a problem with the backlighting which may mean that there is either a loose cable connection from the systemboard to the LCD screen or a faulty LCD screen.
If there is no display at all then there is either a loose cable connection from the systemboard to the LCD screen or a faulty LCD screen.
If you turn on the phone and suspend the display timeout feature and then just leave it there without touching it, does the display still disappear?
If not then holding the phone or movement is causing the problem, again pointing to a loose connection.
If it still disappears then again it can either be a loose connection or a faulty screen.
Here is a link to the Ifixit guide on how to replace the screen in your phone.
LG G3 Screen Replacement