Yuma: I remember that game, but I don't think it involved a No Lynch at LYLO. Just a rules violation resulting in scum win.
The situation we are currently in happened during Mafia VIII. We had, uh, O/me/Galzria/Insomniac/theorel/Yuma still alive. O and me were scum. You, yuma, were confirmed town because you were a vigilante that shot the IC Eevee during the night (thanks!). We knew there were 2 scum left, so we knew that we could No Lynch, likely lose yuma, and continue on the next day if need be. I came out against No Lynching at first, because I was scum and thought maybe I could suck up to you, yuma, since you were likely the one who was going to die.
Ultimately, Galz didn't hammer me in time, so we No Lynched by default. O and me shot yuma. The next day, I got lynched. Ultimately, scum O won it for us, but I don't remember which townies were at fault.
So, No Lynching didn't hurt the town, since they ended up just following through on the same lynch, me.