The problem is:Keep going for No Lynch until the Mafia (in this case the Contract Killer) gets frustrated.
We could go for it at least for a couple of days.
A) There is a rule about not allowing "No Lynch" for consecutive days.
B) There is no investigative role that would threaten the scum. So he can go along with it as long as he likes.
Wonder how you missed that point when it was mentioned in the OP itself.