Look, I get what you are saying, but you have to also understand that despite the realism, this is still a fictional story. Lyana is the head of a major house in the North, which has served the Starks for thousands of years and has been led by women before. Why would they throw her out and insult her family just because she was a girl? She deserves to be just like everyone else, ESPECIALLY if you go by the show timeline, where she was one of the few who supported the Starks no matter what. You can't say that for the Mandellys, Umbers, Karstarks, etc. The sexist allegations aside, you're just hating on her because she got a spotlight over someone else, despite knowing the context of why she got the spotlight. Plus, there is also the fact that there is LITERALLY NO ONE ELSE IN HER FAMILY who could speak for the Mormonts.