What is the chain of command starting with the state governor or a state??

Probably some variation by state. The Lt. Gov. is not in the normal c of c, butt takes over in the protracted absence of the Governor, when necessary.
The rest is pretty much covered by the Secretary's of the major Departments.
Like Transportation, Social Services, General Services, Environment, Corrections and/or Public Safety, Legislative Affairs. That's what I have seen.

Like the VP the Lt. Governor does his own thing, but then takes over if the Gov dies or steps down, as recently happened in NY