Yes, the Lucifer TV series is based on a comic book series of the same name, published by the DC Comics imprint Vertigo. The character Lucifer Morningstar was originally created by writer Neil Gaiman as part of his series The Sandman in 1989. Mike Carey wrote a spin-off series titled The Sandman Presents: Lucifer in 1999, then wrote a Lucifer solo series for 75 issues that ended in 2006.
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.