re:"Is lucifer actually connected to dc?"
It's DC but it's not connected to other DC television series (as of right now). To give a Marvel example, both The Gifted (2017) and Inhumans (2017) are Marvel television series but they are not connected to each other. (Inhumans is part of the MCU but The Gifted is not. The Gifted is an X-men series, which is Marvel, but is not part of the X-Men movie-verse.) Same way, Lucifer and Arrow are both DC series but not connected to each other.