I don't imagine you'd hear huge interference but it's hard to say for sure.
are you driving it from the parallel port? or from a microcontroller or something?
if you're driving it from the parallel port, does the software support 4-bit mode? (it's not exactly significantly harder to program, so many LCD plugins i've seen support it)
another option is converting the LCD to serial, and running it on only one signal wire but that depends on how much you like microcontrollers.