BSD, IMHO:
I’m using “lishmah” to be le’afukei feministic reasons, which are the likely motivating factors if she’s not learning due to “an unquenchable thirst for Torah knowledge” as you proposed before. If shelo lishmah implies femenism – which I strongly believe it would – then yes, it would be assur for a girl to learn shelo lishmah, and “ein mitzvah baah biydei aveira” knocks out “mishelo lishma ba lishma” for girls in this case because it’s a davar sh’eino metsuvah. There is no precedence, that I’m aware of, of using “mishelo lishma ba lishma”, (which is not a pashut heter legabei learning Torah even for men) for a davar sh’eino metzuveh.