That's an interesting question Dex, a candidate for the intelligence question/answer thread
I did only a little looking around. The petalia is a protrusion which in humans tends to favour one side or the other of both the occipital and frontal lobes. Further to that, the protrusions also twist, which the literature calls petalia torque. So far, it appears that this asymetry in hominid brains didn't arrive until
Homo erectus. Perhaps when we began to walk upright, instead of on four limbs, and use implements and tools, handedness became more important?
The literature mentions asymetry in other animals. In capuchin monkeys, the population shows a left-frontal petalia, but no preference to handedness, which seems to be a commonality amongst the new world monkeys.
So, maybe an animal needs both for handedness, which would make a certain amount of sense beyond the simple explanation that we have both lobes with petalias, and these monkeys don't. The occipital lobe is the visual center, so maybe without having a dominant side to the occipital lobe, the hand-eye coordination that plays on our senses and perceptions won't be able to develop a favoured limb.
Interesting question Dex, as are most questions involving the brain