Too bad such a pretty girl, ended up with such problems. I agree, this mare definitely has Lordosis. It is absolutely genetic, so I'll bet her sire and/or dam also had it. It is seen in several breeds, but unfortunately very well entrenched in American Saddlebreds. I've seen many Saddlebreds with the problem and were quite useful riding horses throughout their lives, with careful saddle fitting. I think, I also see a slight hint of a roach there. Others might like to say if they see that, of if I'm just seeing things.
Definitely never allow her to be bred, but give her a chance to do something with her life. She's still very young to possibly have 25 or more years ahead, just being a pasture pet. Keep us posted on her progress and bravo to you, for taking her in.