Law comes in hierarchy, and the lawful are obsessed with it. As such, the Marut will likely prioritize the enforcement of higher laws over lesser laws, and ignore laws not made for it.

So the Marut would ignore the traffic laws made by petty humans in order to follow the greater law of destiny that demands Bob die at this exact moment in time, and it might ignore the law of destiny in order to follow the physical laws that say left must remain the opposite right.

Would they be cold, efficient, and logical or would they be extremely traditional, anal retentive, and OCD?
So in answer to this question, the Marut would be both because cosmic law is not so imperfect that it doesn't have guidelines and contingencies for these situations. A very lawful mortal might not have the benefit of understanding cosmic law as well as a Marut would, but would also strive to be both, and might choose either the option of jaywalking and not jaywalking in this situation without being considered unlawful.