Lilith and Eve have switched places (theory)
Given season 1 has finally wrapped up I think I have enough information to argue that the "Lilith" we see isn't the actual Lilith. I believe at some point Lilith was replaced by Eve in the timeline of events and Eve is now attempting to take Lilith's place in Hell. This could be for a few reasons but we will get to those later.
THE EVIDENCE.
When charlie is explaining the story of Eden and Lucifer's fall we see the shadow versions of Lilith, Adam, and Lucifer (and Sera too). Lilith was the first woman in this story and is drawn in a manner very similar to Adam probably on account of the fact they were made from the same dirt. She has slicked back hair like he does.
We also meet Eve in this flashback and she is shown to be virtually distinct from Lilith. Her hair hangs downward in a manner similar to Vaggies. She might be the blueprint for the exorcists given she was also made from Adam's rib.
The hair orientation is important since we see Lilith and Eve in the same scene and this is how you can tell them apart. They have roughly the same build and probably look the same (probably on account of only being 1 degree removed from each other) but the hair is how you can tell the apart. But that isn't the only difference between the 2.
Lilith is shown to have horns in the flashback, very large ones at that. While this could be written off as the form she takes when using her powers (kind of like how charlie and Lucifer can shapeshift) its also worth noting Lilith is technically considered a sinner because, despite being cast down with Lucifer, she was still created as a human. So far humans have not really been shown to shapeshift THAT much. Alastor's features become more distorted but even when "normal" he still has his antlers. She isn't a Seraphim like her husband or child.
We are even shown a portrait of her where she has them, not using her powers. Grant it, this portrait comes from the pilot and some designs have changed since then. But given Lilith still retains her horns in the story where Charlie talks about Eden... I think its safe to say that this aspect of Lilith still remains consistent. They are even on the "resist" posters. Since she isn't implied to have the ability to retract her horns and her design from what we see changes minimally it should be safe to assume the horns are a permanent fixture of her appearance. Lilith is defined by her slicked back hair and horn.
Does Eve have these things? No.
Lucifers office has several family photos in the background, none of which obscure Lilith's face.
The photo in the middle shows Lilith close with both Lucifer and Charlie. She isn't wearing a hat either but her horns are not visible since the framing of the photo blocks them. However, in the photo to the left of it Lilith is further away from Lucifer and is wearing a hat. This hat does not leave enough room for the horns to exist under it.
We also see this hat motif happen in the pilot as well
We also see in the pilot Lilith diverging from her design quite a bit in this photo which was implied to have been taken recently. The design here might be due to it being not yet standardized when the drawing was made. Who knows. But Lucifer and Charlie are pretty consistent. for the most part. So what the Hell (heh) is up?
Despite seeing Lilith's face MULTIPLE TIMES in both the pilot and the actual show in the form of photos Lilith has her features obscured the next major time we see her in the show (IE during Lucifer's song)
When he takes Charlie away from him we do not see her face, her hair isn't slicked back, and she lacks horns. She is missing both features that make her distinct from Eve. And going back to the hat photo seen earlier in that episode there is no way she has orns under there. There isn't enough space to accommodate.
And of course when Lute goes to threaten "Lilith" at the end of the season: she lacks the horns here too. Her eyes are also not visible and her hair isnt slicked back here either.
Given what we know of Lilith: it would not make sense for her to be in Heaven or help Heaven given she wants to actively fight it by inspiring the sinners to take up arms against them. Realistically, for her character, that would make no sense. It would make sense for her to get frustrated with Lucifer becoming disillusioned but it would not make sense for her to abandon hell or for her to leave her daughter in the dust like she did. Charlie has not seen this woman in 7 years (Which isn't much in hell time) but even if that lines up with the divorce... it would not make sense for her to go radio silent with Charlie even if she did with Lucifer. Charlie is her child. Not unless that wasn't the actual Lilith who did that. I cant explain how but somehow Eve must have taken Lilith's place which would explain this abrupt personality change. While Charlie isn't the most unbiased narrator there are clues to suggest Lilith would not back down that quickly or abruptly especially from her family.
I have a couple reasons as to why Eve might do this.
Theory 1: Lilith is not actually Charlie's mother, Eve was a surrogate
In the season finale Lucifer implied in his battle with Adam that he had sex with both his wives (those being Lilith and Eve respectively). There are also many versions of Lilith's story that make Lilith infertile or cause her to straight up eat/kill children. Why? I don't know. Anyhow; if Lilith was unable to give Lucifer a child its not out of the realm of possibility that he went to Eve to get one given both Lilith and Eve are probably close to clones of each other. Unless in some weird round about way Eve is actually Lute: Eve is probably also in Hell too due to eating the forbidden fruit and doing that whole thing. How Adam isn't I'm not sure. But for Eve it would not be out of the realm of possibility for Lucifer to still have access to her and at some point made a deal with her in regards to that problem. Was this behind Lilith's back? Probably not. They probably both planned that out. However, given we know Adam wanted to be worshipped due to his status as the first man and creator of humanity at large (at least from his bloodline) it would not be out of the realm of possibility for Eve to come back and go "wait, I birthed Charlie the princess of hell so I should be queen since she came from me" and get jealous of Lilith for occupying that position. She, like Adam, is prideful and entitled. She might have been allowed to see and care for Charlie at points when Lilith was away as part of the deal. But I can imagine that Lucifer, feeling bad, gave her an inch and she took a mile and gradually pushed Lilith out unknown to Lucifer. And would he notice? No because the visual differences are minimal and he probably would ration them away anyhow due to him not seeing Lilith for large chunks of time.
Theory 2: Eve replaced Lilith at some point when Charlie was a child
Given none of the images we on Lucifer's wall are dated we have no idea at what point these inconsistencies began popping up. Eve replacing Lilith as a means of gaining power directly for herself (ala Adam only minus the maternal entitlement through Charlie) when Charlie was a child and assuming her role but getting more tired of it/lazy with the charade over time might explain why Lucifer got divorced and why Lilith is absent from Charlie's life. That isn't Lilith to begin with.
I suspect that this act of replacement probably began when the image on the left of Lucifer's wall was taken. This is where we first see that hat design. Charlie looks very young, probably a toddler or a little older, so she probably would not have noticed a difference or at least not one she could communicate well. As for why Lucifer did not notice, again, he has been shown to not really be in tune with whats going on around him. The flashback scene in Lucifer's song seems to take place when Charlie is a little older than she is in the photo. However, I am not sure how fast she ages so this could be decades after fact since Charlie is over 200 years old. By that point Eve or "Lilith" could have been getting tired of pretending and began consolidating power for herself (becoming an overlord of sorts). She might have shown an interest in Charlie for a time due to the fact Charlie was a child and her proximity to Charlie but I doubt it was one that would have lasted as she got older. She might have tried to "adopt her" and keep up the mom act but could not long term hence why she became so distant and then just stopped interacting with Charlie post divorce. This also explains the divorce. While Eve might have had relations with Lucifer once she probably could not stand being around him long term nor inherently liked him very much for condemning her with his "gift". So her "leaving him", especially once when Charlie is an adult and there is no moral guilt of leaving a child, makes sense. That isn't her kid but she would feel bad about it. Plus, why would Lilith (the woman who got away from Adam) want him dead. If anything Eve on account of being around him longer would have more of a reason to want him dead.
Her necklace also looks like an asmodian crystal which allows for shapeshifting.
As for where Lilith is... probably not dead but probably not too aware of what is going on either nor would be given she is probably trapped somewhere.
Theory 3: Something else happened to Lilith and Eve is going to attempt to fill the power vacuum by posing as her
This does not explain some of the past photos but in the event Lilith got killed during an extermination (somehow) or she left for other reasons, Eve could be trying to pose as Lilith to try to control hell from Heaven's side of things by using an asmodian crystal (the necklace we see her with on the beach) to take the form of Lilth and be a puppet for people like Lute or Sera. Both Lute and Sera have motive to want the Hotel to be stopped. And who better to get Charlie to stop than her own mother. This still does not explain where Lilith is or why she left Lucifer; but it explains why "Lilith" is in heaven and why she has done nothing to help her child so far or hell (because Lilith is actually gone).