The Lie derivative of a spinor is defined by

where is the image of by a one-parameter group of isometries with its generator. For a vector field and a covariant derivative , the Lie derivative of is given explicitly by

where and are Dirac matrices (Choquet-Bruhat and DeWitt-Morette 2000).

More things to try:

Weisstein, Eric W. "Spinor Lie Derivative." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SpinorLieDerivative.html