What do I do if my husband is constantly lying to me, and I can no longer trust him to be honest with me? I really want to divorce him because of this.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

No doubt, lying (without any Islaamic considerable justification) is a bad habit and a major sin.  The Prophet warned us against this sin.  He said: "Beware of lying, for it leads to immorality and immorality leads to Hellfire." [Muslim]

We advise you to exhort your husband to give up this sin following the narration of the Prophet who said: "The religion is offering sincere advice."

Also supplicate to Allaah as much as possible to protect him from this bad habit, probably Allaah will bless him to get rid of this habit.  Do not be despair of Allaah's mercy, persist on advising him, be patient and do not give up supplicating Allaah.

You are not allowed to ask him to divorce you even if he does not give up lying despite of all your efforts.  But if you suffer from his lies and cannot bear life with him then you are allowed to take your case to an Islaamic court or to Muslim authorities to weigh the harms you face and to decide accordingly.

Allaah knows best.