How can you work on a marriage with a liar?
ladysheep - it is very difficult, if not impossible, to "work on" a marriage where one partner has made lying to "get what they want" a part of their personality and who they are. It's just another example of "the ends justify the means" sort of thinking.
You CAN remain in a marriage with such a person in the hope that they will change, but it's not likely they WILL change unless they want to change and eliminate lying for themselves. Were you NOT married to him, I would tell you to "run for the hills." But you ARE married. Thus, the ability to "run for the hills" is governed by God's will, not mine or yours.
"Marital Unfaithfulness" is most often thought of as sexual adultery, but it is far more encompassing than that. I don't know your beliefs and I don't know your husband's beliefs, but I can tell you that at the very least your husband needs psychological counseling to address the lying issue. But he first needs to recognize it as a problem for himself(not just a problem in YOUR mind), and I don't hear that recognition in what you've posted.
What you don't need is some "half-hearted" agreement to seek counseling just to "placate" YOU. It has to be about, and for, HIM, by his choice in recognizing a problem and wanting to learn how to change his established "normal behavior."
From your standpoint, God has given reasons why someone CAN divorce, so it sounds like you have "grounds" if you don't see a real chance of things changing. Frankly, unless your husband is willing to surrender his life, totally, to God through Christ, I don't see much likelihood that he will change his "ways" in anything more than a temporary way in order to manipulate you into thinking he's a "changed man."
It is a very tough decision you are facing. Only you have all the facts. But I would seek some good and solid Counsel locally before settling on a "life-changing" decision. You are right though, the "status quo" does sound untenable for long-term happiness and a marriage that honors God.
I pray for wisdom and comfort from God for you, so that you will know God's will in this matter through all your emotional and mental stress. Remember, ladysheep, God is a God of Peace also for his children....that is why even though divorce should be our last resort, it is NOT forbidden. God only says "have a legitimate reason by MY standards, and I will give you Peace. YOUR future is in MY capable hands."
God bless.