lol no, they aren't going to do that on broadcast TV, probably not even basic cable...though i don't know exactly what you mean by follow the comic, because like do you mean the first ten issues or so where it's just Lucifer owning a Night Club and existing in LA, or the next few issues where he frees Michael, chases down his daughter, and goes to war with a bunch of angels and demons and burns down Lux, or like the last fifty or so issues where they create his own universe, it deals with the politics of hell, major battles and plots happen to destroy all forms of creation and God abandons heaven?
it's been doing its own thing in the second and third season that's quite different but fun, they've built up a quality ensemble, the lore has fleshed out
this season has been a bit disjointed because they took four standalone episodes (based around side characters, humans in a number of cases, Mazikeen in one) that were going to end last season after the arc concluded, and reworked them and stuck them into this seasons arc, but starting with the next episode we get back to it and it will have the rest of the extended season, they also used some of those to bring back "lucifer's mom" after the actress turned out to be a great addition to the cast in the second season, though Ella the religiously positive forensic girl is still the best second season addition
lucifer's actually kinda been a bit annoying this season because they retrofit him into more scenes of some of the hold over episodes that were out of place (it looks like had these four been done last year as originally intended he would have barely appeared in two of them, and only as the impetus for a character in another, along with the episode where he and Ella go on a road trip to Vegas), and delayed his own season arc after the second season finale and first two episodes of this season started off running with it as his focus much like the second season where the "case of the weeks" often happened to intertwine with the larger angels/demons plot lucifer was investigating on his own, though they started to lampshade it the last two episodes by everyone, including himself realizing this in the last episode, pointing out how boring he's become and how tired his "i'm the devil!" schitck is...just in time for him to meet the villain of the season and start the season proper
they have done some suggesting that God may have abandoned heaven shortly after Lucy abandoned Hell...Lucifer and Amenadiel are convinced that dad is trying to teach them each a lesson of some kind through events on Earth..."Mum" was exiled to and trapped in Hell by God and got out at the end of the first season, so the second season arc was her reconnecting with "her boys" and plotting a way to get back at her ex and they did some playing around with the "good son"/"bad son" component of the two and what exactly that means if "dear old dad's" directions aren't exactly clear and concise
there's a number of things they've kept true to the comic, like how Lucifer never tells a lie, is offended by all the tales made up about him, especially anything that implies he's not a man of his word, the first season didn't really go there but from the second season on they've made it a point that Lucifer explains that the people in Hell want the torture and punishment out of their own guilt, he never did it for his pleasure it was punishment to him by dad, which is part of why he left Hell, which was one of the comic's premises too
Mazikeen semi-quit as a bartender and became a bounty hunter on the side which seemed appropriate and an acceptable change, also making her the cops roommate and sometimes babysitter...the second season also revealed to Lucifer's therapist that it's not metaphors from a crazy guy, he's actually Lucifer and there
are angels and so on, so that's been fun
in some ways, for the greater myth arc, it does feel like it has gone directions that Constantine could have gone had it continued, especially with the angel character of the first season who mostly did a bunch of cryptic warning and freezing time...but it's stuck closer to the procedural and "fun" aspect rather than dour and doomed nature of Constantine, like Lucifer often gets frustrated with the case of the week, especially if it's not demons or some con or some crazy drama involved to liven it up and tries to hurry things up, and also they brought more characters into the ensemble fully while Constantine only really started to use Zed at the end there
the show was originally adapted by the guy who created/did Californication and while I didn't watch a lot of that I can see the similarities especially in the first season and overall presentation of Lucifer's life during it, but the guy who took over shortly after it started was part of the writers on/or was showrunner on White Collar/Graceland/Almost Human and it's got the same humor as White Collar really...Lucifer is generally like some weird mix of Lucifer, Neal Caffrey and Shawn Spencer
which i guess would make Amenadiel Burton Guster...Lucy even does a joke fake name introduction