What is the ruling on one who swears by the Qur'an not to do a certain thing, and then does it, and what is the expiation for this oath? Is it permissible to lie for fear of envy?

Lying is originally forbidden (haram), but some scholars have permitted it in specific cases. As for lying out of fear of envy (hasad), it is not permissible due to the general prohibition of lying. Lying is not a protection from envy; rather, protection comes through the prescribed supplications (adhkar), prophetic fortifications, and reading the Quran. One can use allusions (tawriya) instead of lying to avoid what is feared.