Fantastic Beasts and Harry Potter are two separate "dimensions" despite being the same universe, only at different times. As are Teen Titans, DC, Power Puff Girls, Scooby-Doo!, etc. If that isn't sound enough for you, the LEGO Batman Movie is the same universe as the LEGO Movie, yet they're two separate "dimensions". The bonus levels in the Gold Brick/Real World dimension imply that they are just LEGO minifigures, being brought to life inside the game, the same as in the LEGO Movie (only with imagination - but even then LEGO minifigures still had some level of consciousness), so it could just be different LEGO IPs as different "dimensions" and not literal universes.
I don't stand by the LEGO Movie/Games sharing the same Batman anymore, it was just a thought at the time, but I honestly don't see LEGO Movie Batman and LEGO Batman meeting up as contradicting the theory