Is expiation permissible for a woman who lied under oath to end an illicit relationship, after her husband refused to divorce her or grant her khulʿ, and he was pushing her to meet other men?

What you did, getting to know a man other than your husband, is an act of betrayal and indecency. You must repent from it by abandoning it, regretting it, and resolving not to return to it. Illicit relationships are forbidden, and if the woman is married, the sin is more severe. Your husband, the dayyuth (cuckold) who allowed this, falls under the Prophet’s (peace be upon him) saying: “Three are forbidden by Allah from entering Paradise: an alcoholic, a disobedient child, and a dayyuth who condones wickedness among his family.”

By requesting khul’ (divorce initiated by the wife), you have fallen into several pitfalls:

1. Requesting separation from a husband who clings to you. The Prophet (peace be upon him) forbade women from doing this without a valid reason, saying: “Any woman who asks her husband for divorce without a sound reason, the scent of Paradise will be forbidden to her.” 2. Swearing an oath about something you are certain is false. This is the yameen al-ghamūs (a perjured oath), which immerses its taker in the Fire, as the Prophet (peace be upon him) said: “The major sins are: associating partners with Allah, disobedience to parents, killing a soul, and the yameen al-ghamūs.” 3. Committing a grave injustice against yourself, your husband, and your children, and falling into a greater error, which is leaving the authority of one man without his consent to the authority of another through a false oath.

What is based on a judge’s ruling, but the underlying reality is different, does not become permissible for its owner, nor does it make something forbidden permissible. Therefore, it is not permissible for you to marry until your first husband makes you permissible for another. If he permits you, then it is permissible to marry someone else; otherwise, it is not.