Yes, interference on the power supply line will cause the Arduino or LCD to crash or be corrupted. You must have a clean power supply, completely independent of (or very well isolated from) any large loads that you're switching, otherwise the switch transients will cause problems. This is a huge issue for all-DC systems, e.g. people trying to control DC motors and servos and connecting them to the same DC supply that runs the Arduino itself, but it shouldn't be too much of a problem for AC systems because you have a switching regulator to isolate your arduino from the mains. Some are better than others, of course...
In your case it sounds like you're getting a big transient off the cooling fan; there's probably something wrong with it if the transient is worse than the enlarger switching. Could probably do with a snubber on the fan terminals.
In your case it sounds like you're getting a big transient off the cooling fan; there's probably something wrong with it if the transient is worse than the enlarger switching. Could probably do with a snubber on the fan terminals.

