Whether her breed matters to you or not, if she doesn't have any sort of offical documentation that she truely is an arab x lip, I would be a little skeptical. Honestly, to me I see some arab but don't really see any Lippizan in her. She moves and looks like an average horse, IMO. If I had to take a guess at what her breeding was, I would say arab x Quarter x TB. But that is just what I see.
The only reason that I really brought this up, is that I often see grade horses that sort of look like a "special" breed and being wayyy overpriced even if they are decently trained, just because the seller says they are an Andalusion or something when it's really just a mustang with no kind of documentation.
If you are fine paying her asking price and the breed doesn't really matter to you to begin with, then that's totally alright ^.^