The best mode to drive an LCD Display to get noise immunity
Personally I would avoid I2C, it idles in a fairly high impedance state with passive pull up which is never good for immunity. 

I would probably go parallel (either 4 or 8 bit it matters not) with interleaved grounds on the ribbon cable, but fact is if you get you grounding right anything should work, this is a slow interface, it is not anything high performance, some simple RC filtering might not hurt at the LCD end just to help the RF immunity, but I would expect to get away without it. 

Your real issue is probably the grounding and wiring around the motor and motor driver, fix that and the problem with the LCD will probably go away, don't fix it and you will be fighting weird glitches for ever.