I felt that the control through Arduino is more reliable at all noise ranges than passive components.
Not sure about that. Not sure at all!
It may depend on how far your LCD is from the Arduino board. Start by putting a 0.1µF (ceramic) and a 10µF capacitor across the Vcc and Ground terminals of the LCD itself.
Now the circuit that the pilot relay (which of course has a "snubber" diode connected across the coil) switches is in no way connected to the Arduino, is it? Because if it is (connected), it provides no
isolation. If the contactor is actuated by DC, it should have a "snubber" diode as well, or if it is AC, it should have a resistor across the coil to draw about 1/10 of the current that the coil does.