Here in Pennsylvania, nobody knows what our Lieutenant Governor does, which would be fine except that it's a separately elected office that's actually in charge of some important shit.
In practice I guess technically we could have an election where all those No Labels voters decide to stick a Democratic Governor with a Republican Lt. Governor, but that would be dumb even if there was any chance of it happening.
We do this with other row offices too where voters have no clue what policy questions hang in the balance in the Treasurer or Prothonotary elections, but Lt. Gov seems like a clear cut case where there's no rationale for an election.
As long as voters just think it's Governor 2, what's wrong with the Presidential model where the Exec candidate gets to pick a running mate?