Reading your post I would say there is a child/parent interaction problem, this is not simply the childs behavior, it would be a good idea to get counselling for you both,you say you both dont get along' so you realise there is also an issue , what does her Dad have to say does he believe she lies.?.
i haven't had to deal with this type of situation. my step daughter lies but only to save herself when she gets in trouble, but as far as lying to make up stuff........
has she had in traumatic experience in her life? Has she been through a divorce? has she always been like this?
Maybe she is wanting attention from you and this is how she gets it. maybe your reinforcing the lies unknowingly. i know some kids will misbehave to get attention cause that's all they know to do to get there parents attention. it's better than getting no attention at all. just like news all they report is the bad or scary stuff. not enough of the good stuff.
try focusing more on her good habits. try positive reinforcement with whatever she does good, like her telling the truth and ignore her lies. when she lies, just tell her you don't want to hear it or just walk away. tell her you'll listen when she's telling the truth. and reinforce that behavior.
she may be mad at you and that her way of getting back. kids act out but it may be for something that seems totally unrelated.
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Find a neutral counsellor and speak to them first. It sounds like your daughter really needs help and I would highly recommend you enter counselling together.