Sooo...Tom Miller thinks Reynolds can't appoint a new Lieutenant Governor.
May 1, 2017
Lieutenant Governor to Serve as Governor, But Lacks Authority to Appoint Lieutenant, Attorney General Opinion Concludes
Formal opinion responds to request by state senator as Governor Branstad prepares to resign for ambassadorship
DES MOINES Attorney General Tom Miller Monday issued a formal legal opinion stating that if a governor resigns, the lieutenant governor becomes governor for all intents and purposes, but does not have legal authority to appoint a new lieutenant governor.
Sen. David Johnson, I-Ocheyedan, requested the opinion following Governor Terry Branstads announcement that, if confirmed by the U.S. Senate, he will serve as U.S. ambassador to China.
The 23-page opinion, following extensive legal and historical research, concludes,
the powers and duties of the office of Governor fall upon the lieutenant governor. The conclusion is based on an Iowa Constitution provision addressing a governors resignation, which states,
the powers and duties of the office
shall devolve upon the lieutenant governor. Under that provision, the opinion adds, The lieutenant governor takes on this authority because she is lieutenant governor.
Significantly, according to Miller, Article IV, section 1 provides that The supreme executive power of this state shall be vested in a chief magistrate, who shall be styled the governor of the state of Iowa.
While the the lieutenant governor becomes governor and has the title of Governor, the opinion further adds that that person does not have constitutional authority to appoint a new lieutenant governor. In other words, upon a governors resignation, the lieutenant governor will hold both the offices of Governor and Lieutenant Governor. There is no vacancy to be filled, according to the opinion.
...
https://www.iowaattorneygeneral.gov/newsroom/lieutenant-governor-to-serve-as-governor-but-lacks-authority-to-appoint-lieutenant-attorney-genera/