There MUST be a reason, why the LCD changes its state. As long as we accept no Woodoo magic to be responsible for, then there MUST be some interference. This the more as you stated, that the micro wasn't addressing the LCD at all with you simple test program!

Now you can check it out:

1. It's a conducted interference, then you WILL see some spikes on the lines which connects both modules, or

2. it's a radiated interference, then you can solve the problem by some simple shielding measures.

Keep in mind, that these LCD modules are little beasts sometimes, being highly susceptible against interference. That the display goes wrong because something was swicthed-on or off at entirely different place is rather common, unfortunately. These LCD modules demand a proper anti-EMI design, keeping the ribbon cable as short as possible. Sometimes it can even be desireable to add buffers with Schmitt-trigger inputs and to insert series termination resistors.
Take care, that interference that hits the LCD display will not see only ONE connection to common ground, means via ribbon cable. This would automatically superimpose any interference to signals. So, use additional connections to connect both grounds (screws, etc.)
Sometimes it can be helpful to feed the ribbon cable through a soft ferrit choke. This will eliminate common mode noise.

Kai