No, Lydia only knows about the Youtube video of the auditioning cellist as a young girl playing Elgar after she's been auditioned and offered the place (subject to a vote from the audience after a trial period) -- she watches the video after they've had lunch together, and that's what prompts her to suggest the Elgar cello concerto as a companion piece to the Mahler, and to ask the current cellists to audition for the plum solo against the new one (Olga?)
All she knows about the new cellist at the audition is that she saw her in the loo beforehand, clearly fancied her, deliberately looked under the cubicle door to note her distinctive shoes, and kept an eye out for them again under the screen at the blind audition -- after which she changes the marks on her audition sheet, presumably to bump them up.
I did think the film pulled its punches there a bit, by making the auditioning cellist Lydia favours demonstrably much stronger than the other auditionee, so there's no question of Lydia forcing through a poor candidate over a stronger one.
And arguably, it pulls its punches again by making Olga palpably so uninterested in Lydia's favours and attention. She's interested in eating as much as possible at lunch, not impressing a powerful conductor, and she blows her off with an excuse about being tired in NY, when she's in fact going out on the town with someone else. It would feel quite different if we saw her falling under Lydia's spell, as Krista possibly did.
I also think it's interesting that we are actually shown the fuller version of the Juillard masterclass, so we know that the edited video that went viral doesn't represent a fair or full version of the dynamic between Lydia and the student.
Todd Field, for whatever reason, does hold back from showing us Lydia as an active, straightforward predator. It's strongly implied re Krista and her assistant (Francesca?), and obviously we see her favour the young cellist -- but the cellist is shown as impervious, not in any way vulnerable. (Though one wonders whether, had Lydia not been fired, she would have manipulated the orchestra into voting not to retain her after the NY trip when she clearly doesn't obtain any sexual favours from her...)