?
I feel the way Oreki acts he could be a town vig or mafia shooter and he wants to get rid of jester because he either has, limitations or x-shots and he is afraid to waste them on a jester. Jester could have bullet proof, or whatever, we don't know what kind of abilities are out there.
Safest bet is to lynch the Jester and shoot other suspects or investigate the main suspects.
Another problem with lynching the jester is that the lynch will stall the mafia hunt and mafia will get two townies down. One through night kill and another townies turns into jester in worst case. Lynching 2 Jester = 3 townies gone.