The answer to this question can be easily found if we look at the final chapter, and the disgust with which Lily's father abandons her to live in a house full of black women. As he goes away, note how Lily turns around and looks at the women who have become her knew mothers:
This is the moment I remember clearest of all--how I stood in the driveway looking back at them. I remember the sight of them standing there waiting. All these women, all this love, waiting.
Lily comes to recognise that she is much better off being with August and her new family than she would ever have been with her father, and she has clearly come to look beyond the colour of a person's skin to see the true individual that exists beneath. This is of course supported by her burgeoning relationship with Zach. Her father has been unable to do that, and his rudeness towards August illustrates that he still thinks that blacks are inferior to whites.