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General relativity and supergravity become integrable systems afterdimensional reduction to two spacetime dimensions. This means the equations ofmotion can be encoded in the flatness condition for a Lax operator. Nicolai andWarner found Lax operators for dimensionally reduced supergravity. They gaveexplicit formulas primarily for the case with $N=16$ supersymmetry in twodimensions (which corresponds to $N=8$ supergravity in four dimensions). Inthis note, we derive analogous results for the case with $N=2$ supersymmetry intwo dimensions (which corresponds to $N=1$ supergravity in four dimensions).This is the simplest example of the general fact that supergravity becomes anintegrable system after dimensional reduction to two dimensions.

A Lax Operator for $d=2$ $N=2$ Supergravity