Kali may actually be a more indigenous resident of India than many of the gods that are hailed in the Vedic tradition. Many of the deities, especailly the male gods, are thought to have been imported by the Aryans who invaded (or just migrated) to India. The indigenous culture was subverted, their gods and goddesses were hidden. It is thought that Kali may be a reemergence of one of these old goddesses. Kali belongs in India more than many of the pantheon. But she was pushed aside, made an outsider, and not looked upon with favor. She lives in the creamation grounds, the dangerous goddess traditionally is too dangerous to be included in society. Interestingly, Siva is thought to have a similar history, also an indigenous god, also traditionally an outsider and a loner, the death of his first wife Sita brought him more into the Aryan and Brahminical traditions, but he was still seen as dangerous, and a little too out there to be acceptable. Kali's reclamation into society is more recent, but she is gradually moving towards more acceptable society. Sometimes this society tried to tame her. Many of the contemporary worshippers of Kali, especially in the West, ignore some of her more fearsome and ruthless cahracteristics. They forget that she still is a destroyer, that wants to destroy.
Lilith on the other hand, is more likely an adopted Goddess. There is a reference in the saga of Gilgamesh to a creature called Lilith, which shares some of our Lilith's characteristics, and she is likely a Babylonia goddess/demon that was adopted by the Jews by contact with the Babylonians. There is one Biblical refence to Lilith, as a creature that inhabits the desert, but it is short, and it is assumed that in the time Lilith was a popular enough figure that people would understand who it was without going into detail, since there is none. Lilith changed with the Jewish adoption, she became Adam's first wife. Some of her demonic aspects were probably already in place, and the Jews just adopted this figure and added what they saw as her history in their own tradition.
Kali and Lilith are very alike. Even though they came from different traditions, and evolved separately, they share much. Both are seductive enough to be adopted by traditions other than their own. One wonders then, is it merely coincidence? Or is there something so deeply ingrained in human conciouness that we have to create powerful female goddesses to fear. Goddesses out of control and destructive, negative examples to warn women who might get try to get too far out of line. We have to create them, and we have to fear them. Sometimes we try to tame them. We tamed Lilith, in a way, pushing her to the side, no longer a goddess of the night but a demonic woman, hiding from people and representing their greatest fears. We are trying to tame Kali in the West, emphasize the mother, de-emphasize the destroyer. But will she let us?