One thing that's interesting is our cool general Tauntaun who is very clearly and openly a hot, long-haired woman, and also a general with a literal post at the front, not just some, say, a weird ceremonial thing.
If this is at least somewhat realistic ancient china, like PLG up there says, how is she a general? This implies men take orders from her. Men have a hard time obeying women nowadays. Military is like THE powerbase and monopoly of violence instrument that men like to keep theirs, even over a rulership position if you note the occasional ruling female queens and other such in medieval europe.
If this is not a realistic china, and instead some slightly more equal fantasy version, and (even if she's really exceptional) people accept an openly female general, how is it a problem if the emperor is not a man? We've at least had like two or something ruling female chinese emperors in real life. Of course it's not impossible the standards might be different, but it feels annoyingly discordant.
I wouldn't be surprised if the author doesn't think about this at all and Lan being a general has no relevance to any sexism or filial piety questions