I am going to guess that as long as your sheep stay on your side of the fence, and your neighbor's sheep stay on your neighbor's side of the fence, then the most that will happen is that the dogs will exchange obscenities from time to time, but that will be about it.
I have found that the LGD is very respectful of territory, and as long as there is not confusion about who's turf is where, they will avoid a battle.
BUT if there is every a mix up because some sheep get through the fence (the sheep do not read the LGD code of ethics), then you will probably have a fight on your hands. If that happens do not try to separate them with anything but water or else you will risk getting bit or risk making the fight even worse. A bucket of water right in the face is the best way to get them apart.
Tamarack Prolific and Ile de France crosses