Is it permissible for someone who has committed a sin to lie if asked about it, in order to avoid publicly disclosing the wrongdoing, even if that leads to swearing a false oath?

The sinner must offer sincere repentance. It is not permissible for a Muslim to disclose their sin publicly, based on the Prophet's (peace be upon him) saying: "All of my ummah will be forgiven except those who publicize their sins." If a Muslim is asked about their sin, they should neither admit to it nor lie, but rather use allusions (ma'areedh), such as saying: "We seek refuge in Allah from that." Whoever commits a sin and then swears they did not do it has sworn a false oath (yameen ghamoos), which is one of the major sins, and they must repent from it.