The lower bound to tire width is really inflation pressure tolerance and rim width...you couldn't go so narrow that the tires wouldn't fit well on the rims. That isn't the case here, so the only practical lower limit is what you'll tolerate in terms of the necessary inflation pressure for narrower tires. For instance, if you currently ride about 60 psi in your 35mm tires, you might need 80 psi in 30mm tires (just as a notional example). As the tire gets narrower (and, thus, shorter), you need more inflation pressure to maintain low rolling resistance and resistance to pinch-flatting.