Yes, Lily repeated year 13, then started a fashion degree in 2017 aged 19, and has now applied to study politics. I don't think that's a lie - although given all the other lies, skepticism is understandable.
Lots of young people change their minds about what they want to study. I don't think the 'picking' is about that. It's more about how difficult Lily is likely to make things for the politics lecturers. Lots of complaints about how trans issues aren't being centered and Lily's identity isn't being accorded sufficient respect, I suspect.