Is it permissible for a wife to seek divorce from her husband after her repeated discovery of his treachery, illicit relationships, and continuous lying to her, knowing that there is an ongoing legal case against him for unlawful seclusion?

This act is a grave abomination, and your husband must repent sincerely from it. We advise you to continue counseling him. If he repents, then praise be to Allah. Otherwise, seek a divorce. If he does not respond, then take the matter to the Sharia judge. If you do not have a male relative (mahram), then seek help from righteous people to assist you.