When you mention livestock you think of creatures such as cows, pigs, sheep, chickens and so on. We've been domesticating animals for like 17,000 years or so and have used them for a variety of means: meat, skins, labor and so on. But would something like this be possible with dinosaurs instead of the mammals we have?
Of course, dairy's not an option with reptiles and using feathers from dinosaurs in lieu of wool from sheep will make the textile industry an interesting one. I'll buy that a nomadic lifestyle would be possible (ie, following the herds), but could a society like ours work with dinosaurs as livestock? I'm looking at all the various species of dinosaur which have actually existed, so no new species have evolved (but they can breathe the same air we do, eat the vegetation that grows here and are able to exist on the same world that we live on now).
And for the sake of the answer, nasty carnivores can be seen as a non-issue (they're either chased off, exterminated or somehow domesticated).