I fix laptops for a living. Generally speaking, when this happens to an LCD panel, you can sometimes figure out a knack of applying pressure somewhere around the screen to fix this, but the problem will usually reoccur when you open or close the lid.
The only solution in my experience is to replace the LCD panel, which is a very easy job. The range in price, generally from about £50 to £120 depending.
Once you can see the back of the panel, you can identify it. You can usually find replacements on Amazon - just search for the part number.
There are only two cables connecting the panel - the VGA cable, and the power cable.
The only exception I ever found to this was on a Vaio, where the hinge had rubbed through the sheath on the cable.
New LCD panel is the only fix usually, though.