In the land of writers and screenwriters, if someone talks about hanging a lantern on something they mean deliberately pointing out a logic flaw in the story to keep it from interfering with credibility. For example, a sci-fi show I occasionally watch has a character notorious for leading the main characters into certain death, often for his own gain. In an episode following one such occurrence, the main character says:
“We must contact HIM. He can help us with this case.”
Now, under normal circumstances, the viewer will automatically roll his eyes and think: “Oh, really? You can’t be serious. Don’t you remember what he did to you LAST episode? Aren’t you supposed to be smarter than that?” (At least those are the sort of things I was saying.) Narrative problems like these make viewers change channels and readers throw books at walls. Unless… you hang a lantern on it.
In the case above, the lantern comes in the immediate dialogue exchange between the two characters:
“HIM? Remember what he did to us last time when he sold us out to so-and-so? You’re really going to trust him again?”
“We have no choice. No one else can do it.”
Thus, the screenwriter anticipated and sidestepped the problem by addressing viewer’s question through the characters. By hanging a lantern on it, the writer rendered the implausible, plausible or at least less of a distraction.