Although I have not read the comic book upon which the series is based, I have watched every episode of Lucifer on TV. The main character, Lucifer, is a Christian concept; in the show, there are very frequent mentions of God as Lucifer's father. However I have never heard any reference to Jesus Christ. According to Christianity, Jesus is the son of God and the savior of humanity -- his absence here seems to be deliberate. Can anyone explain this omission?
I think there are two things going on here, one thematic, and one a production concern.
The idea of the show is about Lucifer and his relationship with God. That relationship and that story played out long before Jesus was born. In that sense, bringing up Jesus would merely be a distraction. Since the show seems to align pretty nicely with traditional he Christian theology, from Lucifer's standpoint, Jesus was just his Father taking physical form on Earth. It's unlikely that Lucifer considers that period of time particularly significant. What he's more focused on is the image of himself that built up afterwards, over the centuries, which is why he abandonded Hell.
On top of that, fictional shows that are based on real-world theology are usually very careful to avoid being too on the nose about it. You see this not only with Lucifer but also similar "modern fantasy" shows like Supernatural. What the show's creators are trying to do is to carefully avoid bringing up anything that would cause "too much" controversy about their show, and cause a public relations issue.
The basic existence of angels and demons, for example, is generic enough that it's not too problematic to include them in a show that's obviously fiction. The idea of an all-powerful God is a bit sketchier, but as He's generally spoken of in vague terms, it's also not a big deal.
Having an on-screen character that is explicitly the Christian devil, with his traditional fallen angel backstory, is really pushing the line. To those people for whom Christianity is a true theology, such a different, and largely comedic, depiction of a part of their faith could be considered offensive. (I know of at least a handful of devout Christians who really dislike the premise of the show as "humanizing" and "trivializing" the concept of Hell.)
The intentional avoiding of mentioning Jesus is almost certainly done to avoid crossing over that line any further than it is. You would need to somehow fit Jesus -- the most important figure in Christianity -- into this show that takes almost nothing else about its own mythology seriously. That's probably a can of worms the writers don't want to open up.
Having said all that, I feel like there's been at least a couple of times that Jesus's existence on Earth was mentioned by Lucifer, though not by named. Again, it would not have been anything the show would want to focus on, but I don't think they are acting as if it never happened.
A straightforward explanation is that the comic book the series (3 series building upon each other, but written by 3 different authors actually) is based on also does not mention Jesus Christ in any significant way.
I do not think the comic authors would be as worried about offending people since the comics just don't have the visibility of a TV show.
That leaves the in-universe explanation, and I think the answer by @KutuluMike has it just right: Lucifer's beef is with God, the concept of predetermination, and of subservient worship, and he rejects them outright. He is not much interested in the finer theologic points that humans have made about these concepts where Jesus might be relevant.
Lucifer became what he is because of events that played out long before the time of Christ.
There are many religions beyond Christianity which believe in a "God" and a "Lucifer", where Lucifer's primary occupation is to reign over a "hell".
Suggesting that Christianity has these two characters, then inferring that other characters from the Christian perspective should also be present is a logical fallacy - projection.
Unless there is other evidence in the TV show that the show subscribes to a Christian perspective then there is no reason to believe that the show must, or should, contain other characters from the Christian perspective.
As designed, the show appeals to people of many faiths. Were they to include a Christ figure, it would suddenly not apply to Muslims, Jewish, agnostic, and audience members of many other religions.
By keeping the show very restricted to an underworld character and a limited view of a deity, it has much more broad appeal.
The show has a much wider base for its lore than just Christianity
Jessica, you say...
According to Christianity...
Well, Christianity is a human cult. All religions are just that: human inventions.
This show is not about what humans believe. This show treats the divine and the demonic as a reality that does not slavishly adhere to what humans believe. And the show frequently makes it plain that what humans believe is very rarely accurate (especially regarding the ruler of Hell).
To add to that, Christianity is only one of the cults that are based on the Abrahamic god and the surrounding lore. Judaism does not recognise Jesus as the Messiah or even as a prophet. And while some branches of Judaism recognises Satan, none recognise the Devil. Islam recognises the Devil, and sees Jesus as a lesser prophet, but not as the Messiah. Yet all these religions — and their sub-versions — are based on the same lore as the show.
So to summarise: yes, Christ is important to Christians... but this show bases its lore on concepts and characters that are far wider than only the Christian mythology. And in any case the show does not consider any particular religion as being rock solid canon and allows itself to adapt that lore as it sees fit.