Not following this case, and only glanced at that filing, but if Lake or someone else has filed a petition for a writ of mandamus, this is likely normal in Arizona practice.
Traditionally a petition for a writ of mandamus is directed against the lower court judge, who would be styled the respondent or defendant. In federal practice this was changed in 1996 so that petitions for mandamus are now styled "In re [name of petitioner]. See Rule 21 of the Federal Rules of Appellate Procedure.
The notes to the 1996 revisions to Rule 21 explained the change as follows:
Notes of Advisory Committee on Rules—1996 Amendment
In most instances, a writ of mandamus or prohibition is not actually directed to a judge in any more personal way than is an order reversing a court's judgment. Most often a petition for a writ of mandamus seeks review of the intrinsic merits of a judge's action and is in reality an adversary proceeding between the parties. See, e.g., Walker v. Columbia Broadcasting System, Inc., 443 F.2d 33 (7th Cir. 1971). In order to change the tone of the rule and of mandamus proceedings generally, the rule is amended so that the judge is not treated as a respondent. The caption and subdivision (a) are amended by deleting the reference to the writs as being “directed to a judge or judges.”
Presumably the Arizona courts are still using the traditional style.