In the past five days I have read the first four trades. This amounts to issues 1-28 of the comic. If I had the fifth volume right now, I wouldn't be writing this.
Lucifer is a spin off from Sandman. Lucifer was a character in certain storylines in Sandman, and one of the things that happened there was that he abdicated Hell, and had Dream, of the endless, cut his wings off. If you have read any Sandman at all, you know that not only is it very well written, but it is also a very dense and I would say fertile work. It is very thick with characters and worlds and possibilities. As you read Sandman, you get a feeling that all of those places existed outside of the storyline, that they were real things with their own histories and futures, and that
whatever we saw in the comic was just a glimpse. It is a very rich work in that regard. There are a lot of possibilities for stories that could be picked up and told. Some of them have been, and many have not. According to the introduction in volume 1, Lucifer is the character that Neil Gaiman most wanted to see 'spun off'. I think it was an ideal choice for that honor, and I think it is clear that Mike Carey really was the right person to do it.
The character of Lucifer is one that I think would be hard to write well. He is clever and sly, he is an individualist, as well as a being of great power. He is called the prince of lies, but as the comics make very clear, he keeps his word. His intellect and his cleverness are such that he seems to operate exclusively in the 'very big picture' view of things. You may think you have him at a disadvantage, but you can't be sure he hadn't already allowed for that, and built it into his plan before you even started to formulate yours. He is a master of negotiation, a master of the bluff, and he is always aware of the true rules that govern any situation. He also commands respect, and may not tolerate it when people don't know their place.
The beauty of this series is in the telling. When you are reading it, you are always seeing multiple angles. You are never perched on Lucifer's shoulder for very long, but you see the plot building through the points of view of a great number of supporting cast. Sometimes the supporting cast are recurring characters, and sometimes they are almost just incidental. In one, we see two unfortunate 'pilgrims' who happen into Lucifer's home uninvited, in another we get a wonderful story of a female centaur that was born in Lucifer's realm outside of creation. She sees the future and seeks to warn him as he is their creator.
My favorite character in the stories is Elaine Belloc. When we first see her she is a young girl whose friend was killed, only to remain her friend as a ghost. Elaine sees ghosts, and is able to call on the spirits of her Grandmothers to give her guidance. We learn a lot more about Elaine as the story goes on, and due to his saving her life and always being honest with her, she is considers Lucifer her friend.
Ultimately the stories relate to Lucifer's rebellion against heaven, and his desire to have a creation of his own where no-one bows down to anyone, and religion is the only thing that is truly forbidden. He makes a lot of enemies in the process, and their machinations are rolled into the story as well, creating a compelling and interesting series of stories and events.
I truly believe that this series is brilliantly done. I would say that it is every bit as good as Sandman, but I think it's standing as a byproduct of that series makes it hard say that. It's the flawless heir in my opinion, a very worthy offspring to a very good comic. It takes the character (and some of the supporting ones) and continues them in a way that just moves naturally from everything we saw about them in the first place.
I strongly recommend giving this a read if you haven't already. If you aren't a Sandman fan you should give it a read anyway. (If anything, just give Sandman: Season of the Mists a read before you start this).