In 'The Lego Movie 2: The Second Part', we're introduced to a new character (Rex Dangervest) who shows up early on in the story to help Emmet on his journey to save his friends. Emmet quickly begins to idolize Rex as he represents all the manly, heroic traits that he lacks himself. As a source of humor and meta-commentary on the career of Chris Pratt—who voices both characters—Rex is a welcome addition to the series. His backstory and arc throughout the film, however, introduce a huge problem into the world-building of the franchise. In my opinion, they kind of brick the universe.
Emmet and The Lego Movie
Obviously, the following contains spoilers for 'The Lego Movie'.
At the end of 'The Lego Movie', we learn that the previous events of the film have been playing out in the imagination of a young boy named Finn. We also learn that the villain of the story (Lord Business), and his goal freeze the world into perfection using The Kragle (a tube of Krazy Glue), represent Finn's father—an uptight business man we've come to know as The Man Upstairs—and his belief that the world can only function if everyone follows the instructions.
The Man Upstairs returns home from work and freaks out because Finn has ruined his perfect world by mismatching his various sets and ignoring the instructions all together. Looking over his son's creation, The Man Upstairs realizes that he is the villain of his son's narrative and has a change of heart. Finn is granted the permission to play with the Lego sets any ways that he pleases and The Man Upstairs embraces Finn's creativity, learning to love a world not governed by instructions.
This ending is quite touching and sort of gives the film a weight it didn't yet have when it was just a silly comedy about Lego people. More importantly though, it establishes the rules of the Lego universe.
The Lego mini-figs are not literally real, but are given life through the imagination of humans in our real world. Sure, in the real world Emmet seemingly wills himself to move so he can gain Finn's attention, but I'd argue this is still an extension of Finn's imagination.
Rex Dangervest and The Lego Movie 2: The Second Part
Obviously, the following contains spoiler for 'The Lego Movie 2: The Second Part'.
At the end of 'The Lego Movie 2: The Second Part', it is revealed that the connection between Emmet and Rex goes far deeper than their voice-actor. They're actually the same character AND this is actually... a Time Travel Story?
On the first loop through the story, Emmet crashes his house-ship in the asteroid field and is lost to the wasteland below the real world dryer where he is lost and abandoned. While he is there he "gets hard" (becoming Rex), wills himself to life without the power of the children's imagination, and constructs his own time machine ship using parts from a Lego version of Doc's DeLorean, Bill & Tedd's Phone Booth, and the TARDIS.
Rex then travels back in time to Emmet's journey through the asteroid field and saves him creating the second loop through the story. His initial goal is seemingly to help Emmet save his friends, but when he learns about the threat of Our-Mom-Ageddon, he decides to work against the group to cause it to happen so all would suffer as he did under the dryer.
Lets snap off for a quick tangent on the Systar System
We need to take a quick break to talk about the ramifications of the Systar System. In 'The Lego Movie 2: The Second Part' we have our first case of competing narrators in the series. In the first film, the entire in-universe world was being created by Finn's imagination. The actions of his sister (Bianca) affect the world—for example the attack of the beings from the planet Duplo—but he drives the narrative. In this film, part of the narrative takes place in the Systar System without Emmet, Rex, or ultimately Finn present. This means that for those sections of the story, Bianca's imagination is driving the narrative. This will be important going forward.
Back to Rex Dangervest bricking the Lego-verse
Now where were we? So at the point where Emmet first enters the asteroid field, we're watching the narrative unfold through Finn's imagination. Bianca has invaded and captured several of Emmet's friends and is blasting off to head up stairs to the Systar System. Finn grabs Emmet and his house-ship and follows after her. It's at this moment when Bianca swats the ship out of his hands—an analog for colliding with the asteroid—and Emmet is launched under the dryer and lost for... years?
While reciting his backstory, Rex claims to have been neglected under the dryer for years. It's his anger over this neglect that willed him to transform himself from the weakling that was Emmet, into the manly hero known as Rex Dangervest. This creates some pretty big issues narratively. Finn was holding the ship when the collision happens. Even if he didn't see Emmet land under the dryer, he knows he was launched somewhere and would undoubtedly begin a search for his favorite figure, "The Special". The idea that his sister knocking a Lego mini-fig out of his hand would be enough for him to forget that mini-fig for years is absolutely ludicrous.
Don't forget that we have a timeline for how much time passes during this story. Our-Mom-Ageddon is a literal ticking clock which we later learn is counting down to the forced boxing of all the Lego to punish the children for not being able to play nicely with each other. This means that, time travel or not, this entire story will play out and resolve in a couple hours... not years.
Even if we take for granted that the "years" Emmet was trapped under the dryer for are imagined, we still have an issue. Lets pretend that Finn saw exactly where Emmet landed, but simply imagined a scenario in which he was lost for years, grew up into Rex, and traveled back in time to prevent him from being swatted down in the first place. The problem here is that Finn cannot actually time travel in real life. He could fish Emmet out from under the dryer, rebuild his ship, grab a new mini-fig for his imagined Rex character, pretend that figure had been lost under the dryer for years, disassemble all his dad's time-travel sets, build his new time travel space ship, and THEN imagine Rex going back in time to stop the ship from crashing in the first place.
Even if we allow for this being the order of operations in the story, it doesn't explain why Emmet wouldn't have just (in universe) rebuilt his ship and taken off after his friends without needing help. It's a running joke in the film that the house keeps getting destroyed, so it would just be like any of the other times he'd had to rebuild it. Additionally, without his sister physically present in the basement—she was at this point up stairs trying to marry Batman and Wa'Nabi—the asteroid field wouldn't exist anymore. He would be able to freely re-build his ship and mount a rescue mission for his friends. A mission that could succeed by him simply swooping in and capturing his friends back.
Instead, the film needs Finn's anger to boil over and cause him to physically destroy his little sister's creations in order to bring about Our-Mom-Ageddon. Given these actions would be out of character for Emmet, the story invents the character of Rex to steer Emmet off course. I'm not sure that a child of any age would be self-aware enough to custom build a new mini-fig to off-load his anger to in order to hide blame for his actions.
Rex Dangervest is a rogue operative in this story. He exists purely as a device to drive the plot forward and not as a logical progression of Finn's imagination. In other words, he bricks The Lego Movie universe.