The car, ____ lights had been left on overnight, wouldn't start.
As a professional writer, I've found that the best way to handle an awkward sentence is to rephrase
(rather than guess)
I agree with Sally. But what makes this hard is it sounds right to use "whose". But that sort of personifies the car, and sounds a little weird.
I too agree with Sally. That is just an awkward sentence that needs to be rephrased. Perhaps "whose" would work when talking about Christine or Herbie.
Sally is correct, but I have seen whose being used for objects. In future, I would like to see 'whose', since it simplifies things.