On September 21, the New York State Court of Appeals, the highest state court in that state, ruled that Governors may appoint new Lieutenant Governors when that office becomes vacant. Therefore, Governor David Paterson’s appointment of Richard Ravitch is valid. Skelos v Paterson, no. 183. Here is the decision.
New York was without a Lieutenant Governor after former Lieutenant Governor Paterson became Governor, due to the resignation of the previous Governor in the middle of his term. Thanks to HowAppealing for the link.
I get the sense that what the court said is as long as the law doesn’t say you can’t you can.