This may seem like a duplicate of this question, but information from The Lego Movie 2: The Second Part seems to provide a different take.
In The Lego Batman Movies, there are a couple references to the events of The Lego Movie, notably the fact that Batman is a master builder and that the city is built on a table. From this movie alone, one would think that The Lego Batman Movie is part of the Lego Cinematic Universe.
However, Lego Movie 2 indicates that after The Lego Movie,
Bricksburg descends into chaos and becomes Apocalypseburg. The Justice League (apart from Batman) has ventured through the Stairgate. Batman seems to be living with Alfred in a Batcave as part of Apocalypseburg.
So the movie seems to address Lego Batman Movie as occurring (mentioning Batman is having a stand-alone adventure) while also ignoring most of it (no Gotham, no Robin and Batgirl, no Justice League party at the Fortress of Solitude, etc.)
Did the events of The Lego Batman Movie occur as part of the Lego Cinematic Universe in between The Lego Movie and Lego Movie 2?