Is it permissible for parents to prevent their daughter from marrying a competent man because he refuses to provide his ex-wife's phone number? Is this considered 'adhl (preventing a woman from marrying a suitable suitor)? And is it permissible for the daughter to lie to her parents, claiming she spoke to her fiancé's ex-wife, in order to avert this injustice?

If the man proposing to you is pleasing in his religion and character, and you have agreed to him, then it is not permissible for your family to reject him. Their demand to ask his ex-wife about him is blatant arbitrariness. They must inquire about him from those who have associated with him, such as his colleagues, neighbors, and friends. If they insist on asking his ex-wife and reject him for this reason, they have fallen into the forbidden 'Adhl (undue prevention of marriage), which incurs sin and invalidates their guardianship. As for claiming to have contacted his ex-wife, this is a forbidden lie, but you can use indirect speech (ma'arid) and dissimulation (tawriya). If indirect speech is not effective and lying becomes the only means to achieve the benefit of marriage, then lying is permissible at that time, as the imams have stated. Speech is a means to achieve objectives, and what cannot be achieved except through lying is permissible in that case.