Put a couple of bypass capacitors (0.1µF + 10µF ) across pins 1 and 2 of the LCD panel. This is a commonly reported problem here.
There are a few tricks to the layout of the relay control circuits. Keep all supply wires and those to the relays together, do not allow loops to form. The relay control transistors, the 1N4007 diodes and the 47µF(or more) bypass capacitor across the 12V relay supply should all be together and all the grounds should connect together in this place.
It may seem counter-intuitive that the "kickback" diode not be connected directly across the relay coil but in fact, the current in the wires to the relay does not change rapidly on (either switch-on or) switch-off (due of course to its inductance) so these wires have little potential for inductive radiation. It is the current in the transistor and the bypass capacitor which changes abruptly, so those three components which carry that impulse current should be kept tightly together and be restricted from any possible ground loops.