The dissension spilled into violence, and the violence to bloodshed. To this point, the traditional Nephite polity is maintaining control, because they are able to drive out the dissenters. It is no surprise that the dissenters would go to the king of the Lamanites. Not only is that likely the next closest polity, but it is probably the one that is providing the model that the dissenters wanted to copy. They go to the king of the Lamanites both because they were driven from Nephite territory, and because that is the type of society they wanted in the first place.