Not just a fan but Lucifer's character design is also inspired from David Bowie. From Wikipedia:
In the earlier related series The Sandman, written by Neil Gaiman, Lucifer abandoned his lordship over Hell. While Lucifer had previously appeared in various stereotypical guises in earlier DC books, Gaiman's version was premised on English poet and prose writer John Milton's Paradise Lost. At Gaiman's request of the artist, Lucifer looks like David Bowie at the time.
“Neil was adamant that the Devil was David Bowie,” recalled artist Kelley Jones in an interview about his work on Sandman. “He just said, ‘He is. You must draw David Bowie. Find David Bowie, or I’ll send you David Bowie. Because if it isn’t David Bowie, you’re going to have to redo it until it is David Bowie.’ So I said, ‘Okay, it’s David Bowie.’”
For why they made him David Bowie fan, refer nerdist.com:
“David Bowie was what the original character was based on, the sketches and stuff that was in the graphic novel,” Ellis said at the 2016 TCA Winter Press Tour. “What we did do is take some of Bowie’s music and infused it into the pilot. Lucifer is a massive David Bowie fan. Music is a massive part of the show. It was a big thing in the pilot script and it’s something we’re trying to continue for the series. Lucifer’s taste in music is a big thing. He’s a big appreciator of music.”