There are legends that Adam had a wife before Eve who was named Lilith, but this is not found in the Bible. The legends vary significantly, but they all essentially agree that Lilith left Adam because she did not want to submit to him. According to the legends, Lilith was an evil, wicked woman who committed adultery with Satan and produced a race of evil creatures. None of this is true. There is no biblical basis whatsoever for these concepts. There is no one in the Bible named Lilith.
The passage most often pointed to as evidence for Lilith is Isaiah 34:14, which in the NRSV reads, "there too Lilith shall repose." This is a poor translation. Every other major translation of the Bible reads something to the effect of "night creature" or "screech owl." Even if "demon monster named Lilith" was the proper translation of the Hebrew word, Adam is nowhere even hinted at in this passage or its context. Whatever the Lilith was, it is not given any connection whatsoever to Adam or Creation.
Another commonly used support for Lilith is the differing Creation accounts in Genesis chapters 1-2. Some claim that the woman in Genesis 1 was Lilith, with the woman in Genesis 2 being Eve. This is completely ludicrous. Rather, Genesis chapter 2 is a "closer look" at the creation of Adam and Eve as recorded in Genesis chapter 1. The Bible specifically says that Adam and Eve were the first human beings ever created (Genesis 1:26-28; 2:18-25). This "Lilith" myth is popular in some radical feminist movements because Lilith is an example of a woman refusing to submit to male headship. While there are myths outside of the Word of God regarding Lilith, her complete absence from Scripture demonstrates that she is nothing more than a myth.