My interpretation of Lily is that he's a male that likes to be cute and got into show business for his father, the point of the backstory being Lily didn't want to grow old and wanted to be young and cute forever, not that he identifies as a girl, so I call him a he. I don't mind people interpreting Lily as being trans, it's possible (though very unlikely, imo) they are. I only have a problem with the obsessive nature of some of those that do - declaring it as some kind of unquestionable fact and attacking anyone that disagrees. You can't even discuss the last episode on every site but 4chan unless you unquestionably agree with that interpretation, any threads about it here get deleted.

It was pretty obvious what they intended.

No Japanese communities seem to think the same way. You're interpreting a Japanese piece of media from western sensibilities.