These things are notoriously noisy, as they generate a high voltage with a primitive generator. You might consider putting a low-value resistor in series with the supply to the generator and bypassing both sides, carefully watching the resulting oscilloscope display. That won't do ALL the work, but probably will enable you to reduce the power to gnd noise to reasonable levels. RFI is another issue. A grounded metal cap might do the trick. A better solution, if other measures don't meet your needs, might be to find a similar LCD with an LED (lower-voltage) backlight.

RE