I have been with my girlfriend for 1 1/2 years and I would like to know if it is possible to trust her since she has lied to me in the past even as such things as having a boyfriend when I first met her?
The only way you will ever come to trust her is through deep and honest communication. Right now you are not getting enough of that. You have little real information to go on. So your mind is running wild with possibilities.
You cannot figure out from what you know right now whether you can trust her or not. But you can attempt to create better deeper and more honest communication with her. And you can know if she responds to that by opening — or closing. That will tell you what you need to know.
If she opens, then it tells you two things: (1) you are creating a safe space in which she feels she can open and be honest; and (2) she is opening, which is a good sign.
It is your responsibility to do (1) — invite her to open in a spirit of safety. You have no control over (2). You can only do (1) and wait and see if she responds.
That will tell you the answer to what you are asking me.