Lucifer's show takes place on an earth where the supernatural, the meta, and the alien haven't broken the masquerade yet. Theoretically all Earths in the local multiverse exist beneath the Sphere of the Gods, where you'll find Heaven & Hell. Lucifer's Mum left the local multiverse. Lucifer continues to chill on his earth doing petty things and hob nobbing with the detective.
Netflix has picked it up and will continue the show.
Constantine showed us the Angel rules of Arrowverse, even though it started on a different network, and those rules seem to be different from the one Lucifer and Amenadiel follow unless they're different as Archangels.
However, Amenadiel and Manny both had similar time stopping exposition powers.
Lucifer's show could potentially be affected by the Crisis and I would love to see this version of Lucifer and Constantine interact. It would be great.