I've always put inflatable pads inside my pack. Rocks are not the only threat: there's also sharp, pointy branches, sticker bushes, and the abrasion of putting the pack on the ground, where it will likely scoot around a bit. Is there anything else you could lash on the outside to make room? For example, you tent poles might lash to the side of the pack, a water filter could go in an outside pocket, etc

Using bungees, if they're the "normal" kind you can buy just about anywhere, also carry a threat. Those hooks on each end can also poke holes in things like pads. If you're going to lash the pad outside, I'd suggest two things: first, make sure it's in a good stuff sack, and second, use the nylon webbing straps with plastic buckles (or a couple lengths of cord secured with knots.)

Not knowing your other gear load, but assuming that it's consistent with the use of a Prolite pad (that is, reasonably light and not too bulky, but not bleeding-edge ultralight), it may be possible that the pack is bordering on being too small for your typical loads. My load is reasonably light and compact, and I find a 48 liter pack is just about perfect - roomy enough for a 4-day trip in the summer, or for the extra layers for a two-night winter trip.