  The KLOE collaboration recently reported bounds on the directional dependence
of the lifetime of the short-lived neutral kaon $K^0_S$ with respect to the
dipole anisotropy of the cosmic microwave background. We interpret their
results in an effective field theory framework developed to probe the violation
of Lorentz invariance in the weak interaction and previously applied to
semileptonic processes, in particular $\beta$ decay. In this approach a general
Lorentz-violating tensor $\chi^{\mu\nu}$ is added to the standard propagator of
the $W$ boson. We perform an exploratory study of the prospects to search for
Lorentz violation in nonleptonic decays. For the kaon, we find that the
sensitivity to Lorentz violation is limited by the velocity of the kaons and by
the extent to which hadronic effects can be calculated. In a simple model we
derive the $K^0_S$ decay rate and calculate the asymmetry for the lifetime.
Using the KLOE data, limits on the values of $\chi^{\mu\nu}$ are determined.
