@Lion is absolutely correct!
You can definitely use her in Connlaoth. 8D There are multiple options to work with!
Keep in mind that, historically, in our world, women have fought in literally every battle, even in patriarchal nations where they weren't allowed to fight, even in nations where the punishment could be death if they were outed. Women have always found ways to participate, and have always fought against and challenged the gender roles of their society. Just because society says, "Women, you can't do this here!" doesn't mean they can't and don't, it just means they face unique challenges and risks.
SotE follows the same understanding. ;D Even if the society for one of our site nations says one thing about gender roles, it doesn't mean people in that society can't and don't break and challenge them! Just like in our real life world.
Women who did this typically cross-dressed. That's the best way to get them IN.
Also, historically, there were cases of women in patriarchal societies where women weren't allowed to serve in the military who, despite that, won over the hearts and trust of the people they lead. Often, the men they lead didn't know they were women at first, but by the time they learned they WERE a woman, they didn't care, because she had lead them to victory enough times and proven herself a good leader. They probably wouldn't have trusted her if they knew she was a woman going in, but if she was later outed? They would trust her, and her gender wouldn't really matter.
I mean, like, the most well known case is Joan of Arc, of course! She faced a lot of criticism and hate from her enemies, but the men she lead trusted her, because she had proven she was a great leader. And there are a ton of other historic cases of women military leaders in restrictive patriarchal societies. It's actually really cool stuff to research because there are sooo many cases--and then so many more we don't actually know about because most women in wars weren't actually discovered except when they were slain on the battlefield and their corpses were being collected. So a lot of historians say there were more women in wars than we actually know, because most
weren't outed while they were alive, and a lot managed to survive and return to their old lives without being discovered.
So I see no reason why that can't happen in Connlaoth. x3
Also, on a lesser level, if a woman presents as a man in the military, gains friends and trust, and is later outed, chances are her friends would cover for her and keep her secret to protect her. Even in horribly restrictive societies, humans are humans. Most people won't try to get their friends murdered. xD Of course, if someone didn't like them and that was the person that discovered things, then that's another story, ahaha.
So tl;dr: women can be soldiers in Connlaoth even if they weren't a Lily/Mordecai. It's just very, very risky!