Those lines are being generated by the graphics chipset. There is nothing wrong with the laptop's LCD. As random as you might feel they are, look again at the image you included. There is a predictable pattern there.
This could be caused by corrupted VRAM, or by the GPU itself. From what I can dig up on model number, the GPU is using 128mb of dedicated VRAM, so you can't blame shared system memory... which is too bad. You should be able to confirm this by connecting an external monitor to the VGA port on the laptop. Bad VRAM will cause the lines to appear on the external monitor as well. A failing GPU can also cause the lines to be replicated on an external... but either way, this is how you eliminate the LCD as being suspect. I'm giving you this diagnostic step to follow to give you more peace of mind, since those lines really do point to (95%) video memory issues.
Since the GPU chipset is integrated into the motherboard on that laptop, which means the video memory is also integrated, you are really looking at replacing the motherboard.