One of my core values is liberty - that means the ability of each individual to make his or her own decisions and live his or her life accordingly

A very sensible value in a heterogenous society, I think. But in this hypothetical nation, everyone is a very good rationalist. So they all, when they shut up and multiply, agree that being a soldier and winning the war is preferable to any outcome involving losing the war, and they all agree that the best thing to do as a group is to have a lottery, and so they all precommit to accepting the results.

No point in giving people the liberty to make their own individual decisions when everyone comes to the same decision anyway. Or more accurately, the society is fully respecting everyone's individual autonomy, but due to the very unlikely nature of the nation, the effect ends up being one of 100% compliance anyway.