Hanging on to the idea that people "shouldn't" lie will only cause distress and disappointment. The reality is that whether they should or shouldn't people lie for a million different reasons. The important thing to do is acknowledge what is real and then create boundaries and make choices accordingly.
If you simply accept that this person lies, then you are at choice point. You then get to decide how you want to interact with them and how to communicate with them. I have found that simple, open, clear, and direct communication will take you a long way in any relationship.
The caution in the communication process is to be careful about your intention/purpose. If your purpose is to get the other person to change, you will only create resentment for both of you. If your purpose is to set a boundary for yourself or to share information, then you have a better chance of creating a better relationship or at least a safer relationship for yourself.
For example, if she lies about something that directly affects you then you clearly and calmly state that you are aware that she is lying and that you do not want to be lied to. You then release the expectation that she will actually hear you and never lie to you again. If her lies are putting your children or you at risk you simply make sure that you create clear boundaries about how she gets to interact with your children or you rather than focusing on getting her to stop lying.
She has to make her own choices about whether lying is an issue for her and unfortunately there is nothing you can do about it. Let her have her own stuff. Does it make it a little difficult sometimes for you? Of course, and then again, you just get to see what choices you have in relating to her, or not, and how that will look for you and your family.