Tracy- My silver bay mare that I show has been treated for Lyme 2 times within a year and a half. I think Lyme is one of those things that once you have it, it never truly goes away. My mare got sick enough before thinking to pull blood for a Lyme test that it was questionable on if she was going to pull through. At somepoint during her being so sick, she lost her ability to sweat. To this day, she still does not sweat, so we have to be careful with her. I cant help you out at all on if they can still be a successful broodmare or not, as I have not and will not breed my Lyme mare where she cant sweat. When my mare showed levels high enough on her bloodwork to treat the Lyme, she was a witch to deal with. She is normally the biggest sweetheart you'll come across. I know to draw blood on her when she has such a change in attitude.
I think like people, Lyme affects horses is different ways. I've had clients treat horses for Lyme and the horse never showed a symptom, never got sick and has never had an issue again. And then you've got mares like mine who got hit hard with it, and the lasting affect of not being able to sweat is not a fun thing for a horse to have to deal with and really limits you on what the horse can do.
I cant help you with the breeding end of of a Lyme horse, but I know my mare to this day still has lasting affects from Lyme.
~Jen~