I would terminate because the lying is a liability for you. She could tell her parents that you do something horrible to her and then you will be in all kinds of trouble. Her parents are doing their due diligence by checking with you about what she is saying but you would think by now they would know how she is and not give her so much power when she tells them something.
The potty training is another story. It sounds like this child is being neglected at home and this is leading to the negative behaviour to get some kind of attention from them. This is a recipe for disaster. Although neglect cases are hard to prove, the not bathing her, having her in dirty clothes is concerning and warrants a call to CAS.