She started in Arithmancy, Ancient Egyptian, Government, and Literature for her electives, though she finished her OWLs for all her classes early. She's continued into NEWTs for Arithmancy and Ancient Egyptian, and tested into Ancient Runes and Latin - she's actually caught up to fifth year for those, plus fourth year Divination. She fully tested out of Astronomy and Old English, going straight to sitting her OWL. Of her core classes, she's kept up with Charms and Herbology at the NEWT level - and she's got an independent study research project into the history of Ancient Egyptian mortuary rituals. She's hoping to finish her Herbology NEWT this year, Potions next - if she can knock out both NEWTs before seventh year, it'd be convenient to use Hogwarts' resources for further study - and she'll probably just replace Latin with Ancient Greek next year - she's also in a book club (mostly for muggleborn students, getting caught up on magical literature) -
(This is a stupidly heavy courseload - normal fifth years have their six core classes, plus two to four electives. Sixth and seventh years usually only take three or four NEWTs, with a capstone project in seventh year, no extra classes. Lily's at three NEWTs (at least one at double speed), three standard classes, and what sure sounds like a capstone, all in fifth year.)