The definition of Lie derivative for spinor fields, in its full generality, requires the introduction of a new geometrical structure, that I called 'super-bundle of geometric objects' in some my related papers published in 1980-81. I have seen that you do not know these my papers. You can find them quoted in this my more recent work: http://arxiv.org/abs/1205.2894 (Part I).
There I generalized this structure in the category of quantum manifolds too.
With compliments.
Agostino Prástaro
Article Concept of Lie Derivative of Spinor Fields. A Geometric Moti...
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