Is it permissible to lie to conceal a sin one has committed secretly, and is this considered one of the permissible types of lying?

The prohibition of lying is well-established through multiple narrations (mutawatir), and lying is a characteristic of hypocrites. Nothing of it is permissible, whether in seriousness or jest. In equivocation (ma'arid), there is room to avoid lying. As for one whom Allah has concealed in their sin, it is not permissible for them to openly declare it. They must repent and conceal their own sin. If they are asked about it, they should not admit to having committed it. They may use equivocation and employ ma'arid, such as saying: "Do you really believe I would do such a thing?" or "Only the ignorant do this," intending their ignorance at the time of the act and their subsequent repentance, or they may interpret their words, such as saying: "I did not do it," intending that they did not do it today.