I think for Day 1, no lynch helps the town because, due to the lack of info, a lynch would be a shot in the dark, right? Thus the probability of a mislynch is high which certainly doesn't help the town...
Lynching is always a shot in the dark since we generally don't have a way of knowing for certain if anyone is mafia or not. Voting patterns are generally the baseline for us to find mafia because it forces mafia to act in ways that can be suspicious, e.g. hammering a townie to secure a lynch or avoiding voting for a mafia (or, in recent games, somehow believing that me hammering a mafia is actually scummy
).
It can be strategic to no lynch if you have something to gain, such as allowing actions to take place. It worked in Kevin's first championship game because the only cops in the game were given extra time to investigate players without risking being outed accidentally by town. The risk is that you basically give mafia a free day (and night if the kill is not stopped), and start the next day with no more information publicly known than the previous day. My take is that each game is different - most games it's not worth the risk, but sometimes it is, and generally it's at least worth debating.
In my opinion, there's not much advantage in this game since the setup is unknown and it's a smaller game, so we don't know if we would even gain anything by no lynching, although we can be sure that we would start the next day still having no information, but possibly still one less townie from the NK. The N0 kill complicates it a bit, but I still think we should focus on analyzing vote patterns, and worry about information later in the game.
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