My answer is pretty cold, but if its guaranteed that he`ll kill again then I`d kill the innocent. One life to save many.
Edited after reading OP in more detail (that'll teach me for skimming an article):
Wait, the townsfolk just assumed the newcomer is the killer/rapist/generally evil doer? So it isnt guaranteed to be him, just a lynch mob going after a stranger? like a "better safe than sorry" type situation? Then no, I wouldn't kill anyone until I get something concrete
Edited after reading OP in more detail (that'll teach me for skimming an article):
Wait, the townsfolk just assumed the newcomer is the killer/rapist/generally evil doer? So it isnt guaranteed to be him, just a lynch mob going after a stranger? like a "better safe than sorry" type situation? Then no, I wouldn't kill anyone until I get something concrete