A threshold question is what role in government the Lieutenant Governor has.
If they're analogues to the Vice President, then their job is basically to be the President's replacement if something happens to them (and to save the President a walk down to Congress to break ties in the Senate).
In that role, I think it makes sense to let the Governor choose who will act if something happens to them, on the condition they're still elected as part of the ticket.
If the perform a separate role, then elect them separately, and the line of succession is incidental.