Should I tell a woman she's a liar?
Do you really think she is?
Yes, I'm sure she's lying just to get what she wants
If you're certain that's what she's doing, then go for it!  People should be called out on lying.  Otherwise they just continue to do it!
It's fine. If she wants to lie that's her problem.
You are right to call her out and if she is lying then let her know why her lie is wrong.