Had this problem too some years ago with a stepper motor controller. The display controller switched off the LCD every time our plasma physicists sparked around (these guys reside six floors below ! ).
Only the power up cycle could bring the display back to life.

Strong filtering (mains filter and DC decoupling with ferrite coil and capacitor combinations) and short wires helped. Keep the impedance of the supply lines as low as possible an avoid ground loops. Use seperate GND wires to connect critical parts directly to the main GND point of the power supply.

All the well known "hints", I know, but they are still true !