short answer: stop using the word
"Lynching" maybe has a fair use case as part of the original Werewolf theme (that 'old village' fantasy/horror setting), which is kind of grimy and horrible overall. When you think of people getting their pitchforks and torches, you think of that setting. So I can see where people think it's a fine word to use.
But we really can't even begin to put the real history of lynchings behind us. Your parents and grandparents were probably alive while people in the US were getting lynched....and if you've never listened to those victims tell their stories of the violence inflicted on their families, you might not understand the really raw anguish that people feel about that word.
We should all be here to have fun, and welcome anybody who wants to play. I hope we don't normalize words that some people are gonna look at and say "okay, nope, that's not for me". The worst thing to do would be to tell someone who might have a real claim to take issue with that word, "get over it, that's just the term we use". Especially as this game can get stresseful, tense, and sometimes angry. How we communicate this language combined with the emotions of the game? It's something we really need to take care and try to understand.
To be honest, "lynch" has never quite fit into the gangster theme of Mafia (and while I'm here, "hooker" is a pretty shitty term to use as well). But I take it you don't want to disappoint anybody who thinks the game thematically needs some teeth to be fun. Feel free to use "kill", "murder", "exile", "banish", or even "evict". I chose that last one for my game because it made more thematic sense, and I think that's a good thing to encourage. I don't think you need to modkill for using "lynch" if the theme is going with something else, but people can do their part to not use it and not normalize the term.
