Both Óscar Romero and Karol Wojtyła (later Pope John Paul II) were viewed as 'non-political' before they were named bishops. This was in part because they were seen as academics without a lot of pastoral experience, and (up to that point) their academics were not the kind of theology that anyone viewed as politically threatening. They both became bishops in countries where the government exerted a lot of influence over the Church, and the Church was very influential to a lot of the people. (Wojtyła in 1950's Poland; Romero in late 1970's El Salvador)
It is safe to say that the Soviets deeply regretted approving Wojtyła as a potential bishop of Krakow at such a young age. The communist government of Poland tried to block his return there, and did not allow him to come on a certain anniversary that they thought would be inflammatory. Instead, Pope John Paul II came for Pentecost, and led the entire country in a nine-day retreat. This led directly to the formation of the union Solidarność. Obviously, he himself wasn't going around forming workers unions or telling people to fight the government. But he could inspire people to bring about change on their own, and this proved rather significant.
Óscar Romero also wound up preaching for change, and was eventually gunned down in his church on account of that.
I'm not saying that either of these bishops should be considered as a model for Lúthien, but I am suggesting that the idea of capturing the spirit of a people and using that to resist evil is a more powerful one than most people traditionally give it credit for. Armies are easy to see and respect the power of. But other methods can also can be hard-hitting and show people the truth that they are defending. Granted, this is typically even more important when a people are being oppressed and their culture is being eroded away or stolen from them to try to force their conformity to a foreign or totalitarian regime. It's not like Doriath has been invaded and is being ruled by a puppet of Morgoth.
So, my concept of Lúthien is that she remembers Beleriand before the return of Morgoth, before the advent of orcs, and before the Girdle. She would want to preserve (there's that elvish impulse) what was vital, essential, and good about the culture of Doriath from that time, and one way to do that is through the Arts. She would want the people to sing their songs and dance under the starlight and remember who they are, and if they are afraid or lose hope, she'd find a way to inspire or encourage them. They can save themselves, but she's going to be the heart of the realm.