There is no Biblical evidence that explicitly states the existence of "Lilith."
Firstly, the majority of translations do not even mention a "Lilith," apart from in the footnotes, make of this what you will, but until everyone learns to translate ancient Hebrew then generally speaking it's better not to assume a mass conspiracy amongst almost all the translators. Also the Isaiah 34:14 passage which is often used, has no reference nor implication (anywhere in the chapter) that it is at all linked to Creation or Adam.
Genesis 1 and 2 are also used to suggest God created two women at the beginning, as in chapter 1 it states "male and female he created them" and seemingly after God's work of Creation was done in chapter 2 it goes into the account of God creating a women from Adam. However, this is why it is important to read anything, including the Bible in context, it clearly states it is still an account of creation (and not after the events already described) at the beginning of Genesis 2:4-7
And then later continues to describe the creation of Eve. That last bit clearly indicates that this is purely a more detailed account of the creation of Adam and Eve. No-one seems to think that God created man twice at the beginning so why believe that he created two women at the beginning. Verse 4 at the beginning is most likely present so people do not take it out of context, as it clarifies the fact that it is still an account of creation described more briefly in chapter 1.
@peterxdunn "Our" does not refer to the object of the sentence (being man) but rather back to the subject, which is a discussion all in itself, this is often thought to be describing God and His Son, some believe it to be God and the angels. As I said that is really a separate discussion (this answer is already long enough as it is, sorry)
Hope that helps =)