During the final encounter with Lady Deathstryke, X-23 is 'let loose' on her and shouts about Julian Keller.
I don't recall anyone from the book called Julian, let alone then encountering Lady Deathstryke.
Who is this person, and why is X-23 so torn up about them?
Julian Keller is better known as Hellion. The same Hellion who is critically injured by Lady Deathstryke when the New X-Men try to ambush the Purifiers.
As for why X-23 is so torn up, Hellion and X-23 may have a history of looking out for each other:
New X-Men team. Just prior to the competition, Emma asked Julian to make sure that X-23 was eliminated early. However, when given the chance to knock her out, he saved her instead, because he owed her for doing the same during a session in the "Danger Cave".
...
During the fight with Nimrod, X-23 was severely injured and was unable to heal herself. Hellion took it upon himself to rescue her by flying to the Institute
It's likely this closeness is one of the reason's why she seems so 'torn up'.