Judge Joseph Lodge, who is a Superior Court Judge in Coconino County, Arizona, will seek re-election as the Libertarian nominee. First he must win the Libertarian primary, but he only needs 15 write-in votes to achieve that, assuming no one else receives more write-ins. No one’s name will be printed on the ballot for that office in the Libertarian primary.
Lodge is a Democrat, but he was removed from the Democratic primary ballot because his petition didn’t specify which seat he was running for. He did have enough valid signatures. See this story. The person who challenged him, Cathleen Nichols, is a Justice of the Peace and also a candidate for the Democratic nomination for Superior Court Judge.
Large-population counties in Arizona do not have partisan elections for Superior Court Judge, but smaller counties, like Coconino County, do. The primary is August 28. Arizona already has one other Superior Court Judge who is a Libertarian. He is John Buttrick, but he is in Maricopa County, which does not have partisan elections for Superior Court Judge.