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The Koopman-von Neumann (KvN) mechanics is an approach that was formulatedlong ago to answer the question regarding the existence of a Hilbert spacerepresentation of classical mechanics. KvN mechanics is a non-relativistictheory, and it is not clear how spin can be included in it, since spin iswidely regarded as a relativistic property. In Eur. Phys. J. Spec. Top. {\bf227}, 2195 (2019) it was argued that the Spohn equation [Ann. Phys. {\bf 282},420 (2000)] is the correct classical framework for the Koopman-von Neumanntheory corresponding to the Dirac equation. However, after L\'{e}vy-Leblond'sseminal work on this topic, it became clear that spin naturally arises alsofrom the Galilean invariant wave equations, without any need of relativisticconsiderations. Inspired by this, we propose another possibility of includingspin in the KvN formalism: the L\'{e}vy-Leblond equation in the Koopman-vonNeumann formalism can be obtained as a null reduction of the massless Diracequation in the Eisenhart-Duval lift metric. To illustrate the idea, weimplement it for a one-dimensional classical system without magneticinteractions.

L\'{e}vy-Leblond Equation and Eisenhart-Duval lift in Koopman-von Neumann Mechanics