I am aware that taking a false oath by Quran is considered a major grave sin and should be avoided at all costs. However, in dire circumstances, is it permissible for a person to take a false oath on the Quran to preserve his/her honour and the honour of his/ her family for a mistake that He/ She made in the past? Meaning if a person was to take a false oath saying He/She was not involved with anyone in the Past (a past mistake which He/she has sincerely repented for), would that be forgiven?
look, if you have the time to do so, make Istikhaara, asking Allah if you should or shouldnt lie, as Allah knows best, and whatever you see and determine to be the right thing to do, do it if it is decreed from Allah the All mighty. the reaos hwy i say Istikhaara is because judging by the situation, it is a pretty big one, and you dont want to lower the status/reputation of yuor family, but at the same time, you dont want to risk taking a false oath, as Allah swt says in the quran:
"Allah does not persecute you for your purposeless (and frivolous) oaths, but takes you to task for your (solemn) oaths which you affirm (deliberately). (If you breach such oaths) the atonement is feeding ten poor persons with an average (quality) food which you serve to your family, or providing them (the poor) with the clothes, or freeing one neck (i.e., a slave). But the one who does not find (all this) shall fast for three days. This is the atonement for your oaths which you affirm (and then break). So, always guard your oaths. It is this way Allah explains most clearly His Revelations to you so that you may become grateful (by obeying His commandments)."(5:89)
also another thing i would like to add is i have heard we shouldnt swear on anything except the name of Allah, so you might want to look into that (i'm not 100% sure though)
General ruling in islam is that sinning should be avoided always, and you should always conceal your sins. But Scholars mention that because of this principle, one may lie when confronted about past sins [assuming doing so does not entail neglect of another’s right, such as not returning stolen money]. Such a lie would not be unlawful.
Yet even when lying is permissible, it would be religiously more precautionary to use misleading words instead of outright lying. [Nahlawi, Durar al-Mubaha]
For example, if asked about a sin in the past that one did commit, one could say, “Alhamdulillah, Allah protected me from that,” intending one’s sincere repentance after the sin, i.e., that Allah protected me from falling into it again…
And Allah knows the best.