I don't think no-lynching is the play here. wagons still generate information and the threat of a player dying is an important part of that information being generated. not knowing the alignment of the player who dies hampers us a bit but its heavily implied that we have something like a coroner to get around that.
Its optimal for us to no-lynch once because it doesn't push back LyLo and gives us another night, but this is only assuming there are no extra kills and no missing deaths. If a doctor successfully prevents a kill N1 and we no-lynch, then we've effectively wasted a lot of the value in that doctor's protection because they would have pushed back LyLo through it if we hadn't no-lynched. Its better to save our no-lynch until MyLo i think, so as to maximize the information we get from wagons and maximize the probability that town's utility can be useful.