Hello there, may I help you?
Having read your situation your daughter seems to have been very insecure and so eager to be accepted that she felt the need to lie in order to be accepted. Children can be very cruel and it seems that your daughter has been the brunt of this due to her lying. She is probably feeling very rejected and unhappy right now and the prospect of having to face these unkind taunts daily can be daunting for any child.
She needs time and patients from you, if there is a child she is friendly with out of school perhaps that friendship could be encouraged, if there is someone at school could they come for tea, have a special outing at the weekend together, a gentle encouragement to allow a friendship to bloom without pushing a situation.
Another point is to reassure her that tings will get better and let her know you are always there for her to talk to if she needs you. It may be worth talking to the school so they are aware of the situation and can perhaps encourage friendships to develop.
Perhaps also allow her to choose a special weekend outing for the family, strengthening confidence, lifting her mood and enabling her to feel emotionally secure and strong to deal with the situation at school.
The most important thing you as a parent can do is to remain calm and try to be patient with her. I hope this is of use to you, please accept if you are happy with the answer.