Just out of curiosity, would this program, as written, be able to support an lcd display? Obviously I would have to get an lcd library and change the serial print information but is this doable?
Yes.
Sometimes relays can make electrical noise which effects the display, but with the proper isolation, shielding, and filtering it can all be made to work if there are problems. The first place to start is with a capacitor across the Vcc/Gnd inputs of the display. Are the relay modules that you have optically isolated? What are they switching, and how are they powered?