Is an expiatory offering (kaffarah) for an oath due from someone who swore to a lie unintentionally, intending to inform another person that his mother was asleep, given that she does not remember for whom she swore, and is not certain whether the oath occurred specifically in this situation or in another, and is it permissible for her to make expiation as a precaution, or to make expiation twice if she suspects the incident recurred?

You must repent from lying. It was possible to use allusive speech instead of lying. As for the oath uttered unintentionally, it is considered a 'laghw' (idle oath) for which there is no expiation according to the most preponderant opinion. However, if you offer expiation as a precaution, there is no harm in it. But if you intentionally made a false oath, it is a 'yameen ghamus' (perjurious oath) which necessitates repentance and for which there is no expiation according to the most preponderant opinion. However, if you offer expiation as a precaution, there is no harm in it. If the oath was repeated twice, and you offer two expiations as a precaution, there is no harm in it. If you doubt whether you swore an oath or not, no expiation is binding upon you. However, if you act cautiously and offer expiation, there is no harm in it, as long as it does not lead to obsessive doubts (waswasa).