All states are somewhat different. It depends on the wording of your state law as to who is named next in the line of succession.
According to the Idaho Lieutenant Governor's website (refer to the link, below), the Lt. Gov. would take over as Governor in the event that the Governor leaves the State or is incapacitated or worse.
The Secretary of State assumes the power of the Governor when the current Governor dies, resigns, or leaves office for other reasons. The current Secretary of State in Arizona is Jan Brewer, a Republican. The current Governor of Arizona is Janet Napolitano, a Democrat, who is currently being considered to become part of President-Elect Obama's cabinet.
The Lieutenant Governor takes over if the Governor cannot complete the term.
The Lt. governor.
If a governor cannot complete their term of office, the lieutenant governor typically takes over and assumes the role of governor.
It depends on the state. Most states have a Lieutenant Governor, who remains prepared to take over as Governor in the event that the Governor cannot or will not complete his/her term, the same way the Vice President remains prepared to take over as President.
The Lieutenant Governor take over.
The Lt. Gov. presides over the Senate, and takes the place of the Gov. if Gov. is unable to serve.
Lieutenant govener
The primary role of lieutenant governors and vice presidents is to step in if the governor or president is not capable of holding office. Each officeholder has specific ancillary duties either expressly outlined or assigned.
The Lieutenant Governor presides over the State Senate with a few exceptions.
The Lieutenant Governor.