I have heard that Lillith was actually the first woman, before Eve. Is this true?

The Bible records the creation of all things, including Adam and Eve, in Genesis 1-2. While Scripture does not pretend to give us all of the details that occurred the story of Lillith may be safely discounted. In Genesis 1:31, after creating both male and female (Gen. 1:27), God looked at all that He had made and pronounced it "very good." The myth of Lillith contains sinful activities (disputes with Adam and illicit activities with demons) that would not have been deemable as "very good." Likewise, since the creation of this woman in chapter 1 is expanded upon in chapter 2 (and the same woman is subseqently named Eve in Gen. 3:20) there seems to be no chronological possibility of their having been such a previous creation as Lillith.

The story of Lillith may be safely discounted as a mixture of ancient pagan beliefs and Jewish superstitions/mythology deriving from the Babylonian Talmud (and further developed by later commentators).

The one possible Biblical reference to a "Lillith" in the Bible is found in Isaiah 34:13-15. In the context however this seems to be referring to some type of wild animal or bird (occurring in a list with other such creatures). (See note 33 in the NET Bible on Isaiah 34:14)