I cannot think a situation in a C9 where a lying townie benefits the town.
Saying that, there seem to be some misconception here.
I think most liars should be lynched. But to me, "Lynch All Liars" implies more than that; it implies you should lynch even liars that aren't scummy, otherwise it'd be "lynch most liars". As a townie, you should lynch exactly those liars whose lynch you expect to help the town more than the alternatives; no more, no less, even if lynching more liars than that prevents future bad play.
Yes, but
1. if he is caught in a lie, his scumminess jumps a lot.
2. LAL doe snot mean you really have to, and obliged to, and simply MUST lynch everybody who lied. If you happen to know for sure he is innocent, of course you dont kill him. Its a metagame ploy, thus, a reason to vote for or lynch the liar, but as all reasons, you dont
have
to listen to it.
Generally you dont have 100% information on anybody. And even if you are 99% sure someone is innocent, if he is caught in a lie, you should modify your assuredness to somewhere 0%-99%, (varying on individual cases).