As far as I can tell, there are only 3 clubs in TN that hold lure coursing events; Chattanooga Kennel Club, Maury County Kennel Club, and Nashville Kennel Club. You can get contact info for these clubs at www.asfa.org and www.akc.org.
Chances are that your dog will enjoy lure coursing and it is indeed wonderful exercise. Only purebred, registered animals may participate in actual competition but most clubs are pretty friendly about allowing any dog to run in practices.
My best wishes to you.