As Jim Hull put it, the Lego Batman Movie cleverly pokes fun at many aspects of story structure, with the "You and I Are Alike" moments, the references to Main Character Resolve ("take a look at yourself and make a change"), and representing the IC Throughline perspective with four different people (Joker, Robin, Barbara, and Alfred), among other things.
I just realized that there's another part of Dramatica that the film parodies, namely the appreciation of conflict (e.g. appreciating what a story point looks like in a particular story, or the conflict itself as opposed to the source of the conflict). In the scene at the beginning where the Joker is getting away and Batman stops him with his grappling hook, we have the following line:
Joker: "Oh yeah? Well, there's only one problem. Who's gonna defuse the bomb? It's got to be one or the other, Batman. Save the city, or catch your greatest enemy. You can't do both."
The Joker just described a great example of an inequity. If his assumption was correct, Batman would be "between a rock and a hard place," or have two things that can't exist in the same place. Of course, this isn't actually an issue for the Dark Knight. When he's told that Joker is his greatest enemy, he replies, "Pfft, no you're not." In other words, Batman is implying, "How is that a problem?" because there actually isn't any conflict there. In a way, the film just poked fun at trying to illustrate story points without actually encoding the conflict (a bad habit of mine ), and therefore missing the entire purpose of such story points.
Once again, this film has amazed me and made me laugh at the same time.
P.S. I left this topic uncategorized because I couldn't figure out where would be the best place to put it.