Typically - upon the death or impeachment of the Governor - or - if the Governor becomes incapacitated and unable to carry out the duties of office (usually set as a period of time by the state constitution).
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 Lieutenant Governor take over.
Yes.
If the governor of Wyoming dies while in office, the lieutenant governor will take their place. The lieutenant governor will stay in office until a new election.
If the governor of Texas dies, resigns, or is removed, the lieutenant governor will take his place until reelection.
The office of Lieutenant Governor is found in the States of the USA. It's purpose is to assist the State's Governor, and take a Governor's place in case the Governor resigns and or becomes to ill to perform the duties of Governor. In a manner of speaking, the office of Lieutenant Governor closely resembles the role in the Federal Government of the Vice President.
The ruling official in state government is the governor, followed by the lieutenant governor. The two are usually of the same political party and if the governor were to for some reason end his duties, the lieutenant governor would take over. Third in line is the Secretary of State.
The Lieutenant Governor will take his place.
I would assume you mean "lieutenant governor". A lieutenant governor can be two things. A lieutenant governor in the US is like a vice president to a governor. They don't really do anything; but they take the governor's place if he can't complete his term. They are often elected together with the governor, like the president and vice president are, but sometimes are chosen separately. The latter can result in weird dynamics - republican governor, democratic lt. governor. In Canada, a lieutenant governor is the queen's representative in each province. Each Canadian province has its own "prime minister", called the premier, and the dynamic is kind of like that of the queen to her PM in that the lieutenant governor has no power over the government but is kind of a ceremonial figure.
The Lieutenant Governor, if the Lieutnant Governor cannot for some reason then it would be the Pro Tempore of the Senate, and if he/she cannot, then the Speaker of the House would take over.
Their specific duties may vary depending on the state and how the state's constitution is written, Their main responsibility is to step up to the governor's position should the elected governor become incapacitated or die while in office.
The secretary of state seems to mostly deal with traffic, and driving. He's almost certainly head of the dmv. and the lt governor does whatever he is told to do by the governor. he has no real duties unless assigned by the governor.