Who is Arthur J. Lux from In the Lake of the Woods and what is their importance?

Arthur J. Lux is the sheriff of Lake of the Woods County, he arrives on the scene the day after Kathy's disappearance and coordinates the search efforts. Lux makes it clear that he isn't willing to go on theories and says that he will noy make guesses about Kathy's fate but will wait for the case to have some resolution.