Lilith

I chose this image for Lilith because it seems to come closest to BPAL's description:

Mother of Demons, Vengeful Fury, Darkest Seductress, Queen of the Djinn, Goddess of the Gate. 

However, there is hardly a creature with more varied descriptions than Lilith. She is in Christianity the first wife of Adam, she is a Jewish  demoness and in modern paganism she is thought to be a Sumerian goddess. 

A prominent translator decided she was mentioned in the Gilgamesh epos, in which she has built herself a house in the huluppah tree from which Inanna wants to make herself a holy throne and a holy bed. I am in no way trained in ancient  Mesopotamian languages, but when I found the original text I was surprised by this conclusion. The original text in our letters (I do not read cuneiform script) is:

sab-ba-bi-a ki-sikil-lil-la-ke e im-ma-ni-ib-du

This is translated as: In its midst Lilith had built for herself a house. 'It' is the tree and in the lines before this we could read how the Zu-bird had made a nest for its young in the crown and how a snake had made her nest at the base. It looks like an interesting trinity and they seem to fit nicely a well-known image in stone:

This image shows the woman with the wings of the bird and with some imagination one could see the coils of the snake in her hands. It is often seen as a depiction of Lilith, the bird feet would be a sign of her being an ancient goddess but for others a sing that she is a demoness.  But just as often it is seen as thin image of the goddess Inanna. The hat is typical for a god(dess) or priest(ess) and ancient goddesses often had bird feet. Of course if Lilith were a goddess she too might have had the hat of a goddess.
But is she? And was she in Inanna's tree? In spite of my lack of knowledge I have my doubts about that. Lets look at the text again: sab-ba-bi-a ki-sikil-lil-la-ke e im-ma-ni-ib-du. I suppose that the Lilith part is where it says 'ki-sikil-lil-la-ke'. But that looks just as much like the word Lilith as it looks like the word lilitu. And lilitu as well as ardat-lili were female demons, part of a family of demons together with the male demon lilu.

Of course, the next question would be: how much difference does that make? What is the difference between gods in a pantheon and demons? Is the only difference that the gods are the good guys and the demons are the bad guys? In that case they would be just opposite sides of the same coin. So perhaps I should leave it at this, as I can not answer my own questions, nor have I found anyone else providing me with an answer that seemed to me to be correct.

So what does Lilith smell like? 

Red wine, myrrh, black musk, and attar of rose.

In its first moments this scent has an overwhelmingly sharp wine-note over myrrh, which shocked me as I thought: "This should smell good, why doesn't it?" But then I remembered a wine note had done that before to me: starting out very sharp, but softening with time. This wine acted the same: after some time the sharpness disappeared and the whole scent became more musky with a warm wine note and the slightest hint of roses. I didn't get much myrrh in that phase, I think it blended in with the musk or the wine. 
Which makes the scent as difficult to place as Lilith herself: it has the sharpness of a demon, but also the enveloping warmth of a protecting goddess.