Well punching was a bit of an exaggeration by me, but the point of getting him to let someone else test the sword remains, no matter how it's achieved.
The point is, Lysander seems to mostly have been pragmatic in his concern about the truth about Sir Worton claim.
He automaticly challenges authority, in this case by challenging the truth of that authorities claim to lead, without actually having much evidential basis for this claim.
The whole Life Campaign, is based around Lysanders search for actual evidence for what was originally just a hunch, in order to stop the lack evidence undermining his authority and allowing Sir Worton to take over.
A Lawful Good character, would likely be more likely not to question Sir Worton's claim to be a Gryphenheart beacause, since well only a Gryphenheart can draw the blade. The initial evidence, supports the claim, initially challenging that evidence, is a pretty chaotic thing to do.
The immediate hunch that the one calling upon tradition to oppose him, is lying, is in a sense a chaotic action, beacause he challenges the validity of the tradition first, and then he finds the evidence slowly.
A Lawful Good character, would likely hand over power, but would turn against Sir Worton if someone came up with evidence that he wasn't what he said he was.
In short, Lysander is Chaotic Good, but aware of the fact he needs Lawful people, to be on his side.