I think that most dinosaurs of LBT think in totally different terms than humans do. I suppose there would be (if at all) only very, very vague thoughts of "owning" territory or the like. So long they have enough to eat and drink most dinosaurs will be perfectly happy and if they don't have enough to eat or to drink most of them would think of moving to a different place rather than trying to kill others to have more food for themselves (which would also be a great risk of getting killed or injured themselves). For example none of the Stegosaurs in LBT 8 thought about ousting anyone from the Great Valley to be able to stay there.
There is of course the racism which might if fostered within a secluded group of dinosaurs (threehorns most likely) might cause them to try to rid the place where they want to stay of any other kind.
There is a kind of hierarchy within herds with a herd leader, but unlike in case of many human societies I suppose a dinosaur would always be permitted to leave a herd if he or she is not happy with the leadership. There may be different types of leaders some (like Bron) being made leader because others just trust and follow him; other leaders might be formally elected, and maybe some are just made leader for being the strongest or the like.
My story "Old Threehorns" is pushing the idea of military concepts in LBT about as far as I think it can possibly be pushed, but it took a lot of explanation to keep it hopefully within what would be realistic in an LBT story.