Lying, at times, can help. It can also blow up in your face. It's a difficult task to chart between the two. But Oswald being Oswald is the best to do so. And if not her, then the others who know her. Which is not you or me.
If when she is informed so that it does her the least harm, she chooses to die, that is her choice. But life and suffering can seem unending, even be unending, without it being preferred to die.
If there is a way you would wish for this to be handled, were it you, you could document what you would want, so your wishes - your agency - can be respected.