Certainly, on some levels, Lee and Holden can be seen as counterparts.  They are both outsiders.  It is evident that neither one fit into the social setting of their exclusive prep schools.  Both also experience the darker side of human nature in terms of broken promises or ruptured bonds.  Yet, I don't necessarily think that they are mirrored images of one another as there are some distinct differences.  One such difference between both is their economic condition.  Holden has moved from school to school and will continue to do so because he is not challenged from a materialistic point of view.  Lee comes from a "less than privileged" setting.  This is something that she has to endure throughout her time at the Ault School.  Others hold it over her and even when it is not dominant, it is present.  This changes her condition and her point of view at the Ault School, and is a dimension that is not evident in Holden's character.  The lack of economic opportunity causes Lee to want to try to fit in more at the Ault school, something that is not as important for Holden, who has seen this same situation before.  

Thematically speaking, Holden is more about making a social statement about human beings, in general.  He is striving for a type of metaphysical truth about what it means to be with people in the world.  His dream of being the catcher in the rye, the closing lines of the work, and the way in which he relates to the world are all a part of this larger understanding.  Lee is struggling with her own being in the world.  She seems to be fighting more of the battle in recognizing her own past in light of her present at the Ault School.  She does not seem to be as driven to making a statement about the nature of humanity as much as she is simply seeking to better understand herself, her world, and her place in it.  This reflects another level in which it is difficult to fully see both characters as exact counterparts of one another.