Who is Liz from Mao II and what is their importance?

Liz is Bill's daughter, appearing in only one chapter. Her presence is the catalyst for narrative revelations of Bill's self-absorbedness, an apparently fundamental characteristic of his nature that he, according to Liz, has carried with him all his life. This self-absorbedness is a fundamental component of his obsessive-ness (see the commentary above on Bill's character).