Unlear if the library guy knew what MC summoned and lied so that the king would kill it or he simply discovered what it was after the summoning, realized he messed up and tried to burn the book.
Is one thing if the MC pops up with a dragon out of nowhere and the kingdom discovers they had a book predicitng exactly that and another if there is no book, the bastard shouldn't be punished if like everybody else in the room he could say there was no info about it.
thing is I checked raws up to chapter 15 and we still don't see what happens after the king hears it.