In the most recent episode of Black Lightening, they made a reference to Supergirl. And one of the characters was reading an issue of the Outsiders. Given this, there is a fan theory that BL takes place on the same Earth as Supergirl. This would also fit with BL's history in Metropolis in the comics. The showrunners have said that it had no connection to the rest of the Arrowverse, partially because it was originally developed for Fox and partially because it's filmed in Atlanta whereas the rest of the shows are filmed in Vancouver. But given that all the other super-shows take place on GA's Earth, would it make sense to sort of share space with Supergirl? Keep in mind that they also did an episode where they reference other heroes on that Earth whereas BL is seen as a vigilante. Other heroes in this case could mean Superman and Supergirl (and to a lesser extent, Batman, since he's been partially acknowledged).