Charles,
Sotomayor is not a “secret” leftist. She is an easily identifiable leftist, simply due to her own words. She has admitted that it is nearly impossible for her to be impartial. In her own words she questioned whether impartiality “is possible in all, or even, in most, cases.” She says this is due to race, culture, upbringing, etc.
So to her, objectivity is out the window. This puts her firmly on the left.
This means that when she takes the oath, she has to lie, as part of the oath requires her to be impartial and objective.