The Zohar is the one ancient work that most firmly establishes the identity of Azazel as the seed of Lilith. As we have seen in our discussion on Lilith, the Zohar is a collection of Kabbalistic Midrashes (commentaries) on the Torah, and as such, the Zohar largely defines Kabbalistic beliefs.
In the Zohar Azazel is nearly as prevalent as Lilith. The Zohar mentions him by name in 19 separate passages and by indirect reference 9 more times, for a total 28 references. This is in comparison to Lilith, which the Zohar mentions by name in 27 separate passages and by indirect reference in a further 29, for a total of 56 direct references. As we have already seen, the Zohar’s commentary on Lilith is consistent with her being the first created woman with Adam from the ground, who became the Serpent of the garden upon rebelling against Adam and God. And as we shall see, the Zohar’s passages on Azazel are consistent with him being Lilith’s firstborn seed.
The most important passage in the Zohar establishing Azazel as the seed of Lilith comes in Vayetze 116 below. The passage is a bit difficult to understand on first reading, as the Zohar is a highly mystical work which is difficult to comprehend for outsiders unschooled in its principles. However, a little study reveals its message.
Vayetze 116 (Vol 9: “And Ya’akov went out of Be’er Sheva,” part two)
From the north side, the grades spread until the dross of gold reaches down TO BRIYAH, YETZIRAH, AND ASIYAH of the unholy side. The unholy filth grasps THE MALE above and THE FEMALE below. Here, male and female join together. They are the rider ON THE SERPENT and the serpent, which is the secret of the male and female. This is the secret of Azazel, WHICH INCLUDES THE MALE AND FEMALE OF DEFILEMENT.
Vayetze 116 states that the secret of Azazel is that he is the “unholy filth” in who is “joined together” Samael (the male rider of the Serpent) with the female Serpent. Azazel grasps hold the male aspect of Samael and joins it together within himself with the aspect of the female Serpent. We already seen that the female Serpent is Lilith, and the male rider is the spirit of Samael.
Calling Azazel “unholy filth” suggests he is derived from a sexual act between Samael and the Serpent. In the Zohar filth is used to describe the defiled semen of Samael and/or the Serpent. For example, Acharei Mot 359 below accuses the Serpent of casting filth (i.e. semen or defiled linage) into Eve, causing her to conceive Cain. This is repeated in Pekudei 203 and several other passages. When Vayetze 116 says Azazel is the unholy filth in which the Serpent and her rider Samael are “joined together”, this implies he is the seed of their union. Just as the DNA and physical characteristics of a human father and mother are joined together in their seed, so too is Azazel the focal point of the joining of the characteristics of the Serpent Lilith and her rider Samael. Note that Acharei 359 states that both Adam and Eve sired demons from the Serpent Lilith. This is possible because of the dual sexual nature of the Serpent.
Acharei Mot 359: Lilit and Na-amah
We have learned that when Adam descended with the supernal image, a holy form, and those on high and below saw him, they approached him and crowned him ruler over this world. Later, when the serpent came upon Eve, it injected its filth in her. Following this, she gave birth to Cain; SHE DELIVERED CAIN FROM THE FILTH OF THE SERPENT. From that genealogy were the subsequent generations of the world’s evildoers and the habitations of demons and spirits come from there and his side. For this reason, all spirits and demons in the world are partly of people below and partly of the angels on high, AS THEY ARE BORN HALF FROM THE FILTH OF THE SERPENT, UPON IT WHICH THE ANGEL SAMAEL RODE. THEREFORE, HALF STEM FROM THE ANGELS. THEIR OTHER HALF IS HUMAN, BECAUSE THEY WERE BORN FROM CAIN WHO WAS HUMAN. These other DEMONS born from Adam THROUGH TWO FEMALE SPIRITS, AS MENTIONED ABOVE, are all similar as they stem half from below and half from above.
Pekudei 203: Breastplate and Efod
After Adam and his wife sinned, and the serpent had intercourse with Eve and injected filth into her, Eve bore Cain. He had the shape from above and FROM below in the secret of the filth of the Other Side, and from the side below OF THE EXTERNAL FORCES. Therefore, he was the first to bring death into the world, caused by his side, AS HE CAME OF THE FILTH OF THE SERPENT. The nature of the serpent is to lurk so as to kill, and his issue, CAIN, learned his ways. And so it is written, “and it came to pass, when they were in the field, that Cain rose up against Abel his brother and slew him” (Beresheet 4:8).
Many of the other mentions of Azazel in the Zohar concern his role in the Yom Kippur ceremony. Some of the more note-worthy passages that confirm assertions in the previous section about Azazel’s role in the ceremony are as follows.
Tzav 42 confirms the notion that the goat to Azazel is a rejected sacrifice that is unable to rise to Jehovah as an atonement. It cannot rise because it is burdened by all the sins of Israel heaped upon it. This goat carries away Israel’s sins. The passage also equates the ceremony’s goat to Jehovah, the accepted sacrifice, to the “perfect man.” This confirms the archetype of Messiah in the goat to Jehovah.
Pinchas 681 confirms that in the goat to Azazel, Samael is separated from everything and bears all the transgressions of Israel upon him. Jehovah is said to be “forgiving (bearing) iniquity”, meaning that he temporarily “bears” the burden of sin so that he might remove it utterly from Israel and place it upon Azazel, upon whom it shall be forever more. This confirms the previously laid-out notions of the Yom Kippur ceremony that Azazel is the seed of the Serpent in rivalry with Messiah.
 Translation from https://www.kabbalah.com/k/index.php/p=zohar/zohar. ALL CAPS text are clarifications and commentary added by later translators of Zohar.