Me and this person really dislike each other and ...

Ignore him. The best thing you can do in this situation is ignore him and ignore the lies he's spreading. To react is to show him you care about what he's saying about you. Don't fan the flames by trying to get people "on your side." Whatever the situation is, it will pass. Just give it time. Good luck!

Hi,

     I  think you should approach the other person and ask her what bothers her about you.  I know this is not easy to do but just tell her that you are aware that she is saying a lot of nasty untrue things about you and if she does not stop this, she may be charged with slander.

   See what she says.  Make her aware that you do not want trouble and would just like to get along with her.

You have to do "Damage control" every chance you get.  Whenever you run into one of these people that have heard these lies about you, pull them aside and let them know what's up!  Tell them to watch their back around this guy because he feels like he has to spread lies about people  to have any friends, tell anyone who'll listen that the guy can't be trusted!  Like who's he gonna start spreading lies about next!?   People like that are such.. @#%&!ers!  Don't let him get away with it!  If you have to, take up Boxing or Karate and kick his ass!  He sounds like a punk!

I am sure you have your own life with set of things to do. As far as it does not bother your day to day life, ignore it.

Get busy with your work, meet people around and interact. People who know you will not believe anybody else.