I'm sorry this is happening to you and I guess that you try depends upon several things, The first being the subject of the lies. I would think it has be be something pretty major to have this effect on you. Would you like to give an indication of what it is about? (You are under no obligation of course, only say what you feel comfortable with). It's just without specific details it might be hard to give you the exact support you need.
A person with a gambling problem is a whole different case from one who goes out for nights with the boys, and our responses would be tailored accordingly.
The real answers to your questions lies inside you, as I'm sure you know. Your desire to remain, your strenght, if you feel cared for.
I feel I do have to mention having depression and an anxiety condition is not good at the best of times and while I hate to bring this up I've often been convinced of something highly unpleasant due to my anxiety condition, things that have turned out not to be so. I'm not doubting you, just raising the point I've been mistaken.
Your experience before with your instinct being confirmed most probably may mean you are right this time too.
It would be good to have certainty either way.
First can I suggest a clear and frank discussion with you partner about how you feel, what it is doing to you and the basis of these current suspicions. It may be easiest for just the two of you alone, or with a councilor.
If that does not resolve matters then I guess you may decide if you should stay or go.I do think being in a permanent state of distrust and anxiety is not going to be good for you long-term.
Look, I've only touched the surface of a complex issue, if you would like to come back and say more that would be great