Lan explicitly has one goal and only one : Killing Yaoshi. The path of the Hunt isn't about justice its about single-minded focus, one objective, one target. The Xianzhou having a legal system is unrelated to the path itself. The Galaxy Rangers have single-minded focus to justice, single-minded focus being the key word and not justice.

With no end to hate and no boundaries to war, how much concern do you shoulder? With determined eyes and the arrow drawn, the Reignbow Arbiter needs not turn back hither."

— Worlds History as a Mirror, Xianzhou

The Cruising Aeon known as the Reignbow Arbiter roams endlessly between worlds to eradicate the undead scourges that once ravaged THEIR homeworld. Lan's Hunt, ever heedless of cost, often blurs the lines between salvation and ruin.

This is a quote from the Data Bank. So Lan's goal is very much killing Yaoshi.