I feel that going without an alignment restriction is the way to go... not only does it fit with the spirit of "Order of the Dragon", as many people have already mentioned, but wouldn't people also agree that it could fit with something like "Order of the Shield"?
Not every single time, of course, but I'm sure there would be plenty of times where a "Cavalier for the Little Guy" could bang heads with a Local Baron's tax collectors, or when an army needs to Quarter soldiers in villagers homes? Lawful-wise, those two examples are not totally demanding, but both require putting country before self, and in this instance, a Cavalier of the Shield might feel that both are too demanding of those under his charge.
I can totally see how people would expect the Cavalier to be either Lawful or Neutral, though, especially with the Oaths and Orders.
But that's just my view.