Hey, boy genius... The King James is one of the many re-writes. Lilith's name doesn't appear in the bible, but it does appear in the oral tradition and Babylonian Talmud, which supplement the Torah... this was long before Christians came along to add their own bits to the Torah and call it the bible.
If you read Genesis 1, man and woman are created in the same passage. In Genesis 2, woman is created from man. The modern Christian apologetic for this is usually that Gen 2 simply details the events of Gen 1, however, long before the KJV came along, it was believed that Gen 1 speaks of Lilith's creation as an equal to Adam, so God decided to try again by making Eve, who is lesser than Adam, having been made from his rib instead.